id sid tid token lemma pos iajs-2703 1 1 58 58 NUM iajs-2703 1 2 solving solving NOUN iajs-2703 1 3 oscillating oscillating NOUN iajs-2703 1 4 problems problem NOUN iajs-2703 1 5 using use VERB iajs-2703 1 6 modifying modify VERB iajs-2703 1 7 runge runge NOUN iajs-2703 1 8 - - PUNCT iajs-2703 1 9 kutta kutta NOUN iajs-2703 1 10 methods method NOUN iajs-2703 1 11 zainab zainab PROPN iajs-2703 1 12 khaled khaled PROPN iajs-2703 1 13 ghazal ghazal PROPN iajs-2703 1 14 kasim kasim PROPN iajs-2703 1 15 abbas abbas PROPN iajs-2703 1 16 hussain hussain PROPN iajs-2703 1 17 department department PROPN iajs-2703 1 18 of of ADP iajs-2703 1 19 mathematics mathematics PROPN iajs-2703 1 20 , , PUNCT iajs-2703 1 21 college college NOUN iajs-2703 1 22 of of ADP iajs-2703 1 23 science science NOUN iajs-2703 1 24 , , PUNCT iajs-2703 1 25 mustansiriyah mustansiriyah NOUN iajs-2703 1 26 university university NOUN iajs-2703 1 27 , , PUNCT iajs-2703 1 28 baghdad baghdad PROPN iajs-2703 1 29 , , PUNCT iajs-2703 1 30 iraq iraq PROPN iajs-2703 1 31 . . PUNCT iajs-2703 2 1 kasimabbas@uomustansiriyah.edu.iq kasimabbas@uomustansiriyah.edu.iq PROPN iajs-2703 2 2 zkgzainab@gmail.com zkgzainab@gmail.com X iajs-2703 3 1 abstract abstract ADJ iajs-2703 3 2 this this DET iajs-2703 3 3 paper paper NOUN iajs-2703 3 4 develop develop VERB iajs-2703 3 5 conventional conventional ADJ iajs-2703 3 6 runge runge NOUN iajs-2703 3 7 - - PUNCT iajs-2703 3 8 kutta kutta NOUN iajs-2703 3 9 methods method NOUN iajs-2703 3 10 of of ADP iajs-2703 3 11 order order NOUN iajs-2703 3 12 four four NUM iajs-2703 3 13 and and CCONJ iajs-2703 3 14 order order VERB iajs-2703 3 15 five five NUM iajs-2703 3 16 to to PART iajs-2703 3 17 solve solve VERB iajs-2703 3 18 ordinary ordinary ADJ iajs-2703 3 19 differential differential ADJ iajs-2703 3 20 equations equation NOUN iajs-2703 3 21 with with ADP iajs-2703 3 22 oscillating oscillate VERB iajs-2703 3 23 solutions solution NOUN iajs-2703 3 24 . . PUNCT iajs-2703 4 1 the the DET iajs-2703 4 2 new new ADJ iajs-2703 4 3 modified modify VERB iajs-2703 4 4 rungekutta rungekutta NOUN iajs-2703 4 5 methods method NOUN iajs-2703 4 6 ( ( PUNCT iajs-2703 4 7 mrk mrk PROPN iajs-2703 4 8 ) ) PUNCT iajs-2703 4 9 contain contain VERB iajs-2703 4 10 the the DET iajs-2703 4 11 invalidation invalidation NOUN iajs-2703 4 12 of of ADP iajs-2703 4 13 phase phase NOUN iajs-2703 4 14 lag lag NOUN iajs-2703 4 15 , , PUNCT iajs-2703 4 16 phase phase NOUN iajs-2703 4 17 lag lag NOUN iajs-2703 4 18 ’s ’s PART iajs-2703 4 19 derivatives derivative NOUN iajs-2703 4 20 , , PUNCT iajs-2703 4 21 and and CCONJ iajs-2703 4 22 amplification amplification NOUN iajs-2703 4 23 error error NOUN iajs-2703 4 24 . . PUNCT iajs-2703 5 1 numerical numerical ADJ iajs-2703 5 2 tests test NOUN iajs-2703 5 3 from from ADP iajs-2703 5 4 their their PRON iajs-2703 5 5 outcomes outcome NOUN iajs-2703 5 6 show show VERB iajs-2703 5 7 the the DET iajs-2703 5 8 robustness robustness NOUN iajs-2703 5 9 and and CCONJ iajs-2703 5 10 competence competence NOUN iajs-2703 5 11 of of ADP iajs-2703 5 12 the the DET iajs-2703 5 13 new new ADJ iajs-2703 5 14 methods method NOUN iajs-2703 5 15 compared compare VERB iajs-2703 5 16 to to ADP iajs-2703 5 17 the the DET iajs-2703 5 18 well well ADV iajs-2703 5 19 - - PUNCT iajs-2703 5 20 known know VERB iajs-2703 5 21 runge runge NOUN iajs-2703 5 22 - - PUNCT iajs-2703 5 23 kutta kutta NOUN iajs-2703 5 24 methods method NOUN iajs-2703 5 25 in in ADP iajs-2703 5 26 the the DET iajs-2703 5 27 scientific scientific ADJ iajs-2703 5 28 literature literature NOUN iajs-2703 5 29 . . PUNCT iajs-2703 6 1 keywords keyword NOUN iajs-2703 6 2 : : PUNCT iajs-2703 6 3 explicit explicit ADJ iajs-2703 6 4 runge runge NOUN iajs-2703 6 5 - - PUNCT iajs-2703 6 6 kutta kutta NOUN iajs-2703 6 7 methods method NOUN iajs-2703 6 8 , , PUNCT iajs-2703 6 9 oscillating oscillate VERB iajs-2703 6 10 problems problem NOUN iajs-2703 6 11 phase phase NOUN iajs-2703 6 12 - - PUNCT iajs-2703 6 13 lag lag NOUN iajs-2703 6 14 properties property NOUN iajs-2703 6 15 1 1 NUM iajs-2703 6 16 . . PUNCT iajs-2703 7 1 introduction introduction NOUN iajs-2703 7 2 this this DET iajs-2703 7 3 essay essay NOUN iajs-2703 7 4 dealing deal VERB iajs-2703 7 5 with with ADP iajs-2703 7 6 the the DET iajs-2703 7 7 system system NOUN iajs-2703 7 8 of of ADP iajs-2703 7 9 special special ADJ iajs-2703 7 10 first first ADJ iajs-2703 7 11 - - PUNCT iajs-2703 7 12 order order NOUN iajs-2703 7 13 ordinary ordinary ADJ iajs-2703 7 14 differential differential ADJ iajs-2703 7 15 equation equation NOUN iajs-2703 7 16 in in ADP iajs-2703 7 17 the the DET iajs-2703 7 18 following follow VERB iajs-2703 7 19 form form NOUN iajs-2703 7 20 : : PUNCT iajs-2703 7 21 𝑒′(𝑑 𝑒′(𝑑 NUM iajs-2703 7 22 ) ) PUNCT iajs-2703 8 1 = = PUNCT iajs-2703 8 2 𝑓(𝑑 𝑓(𝑑 NOUN iajs-2703 8 3 , , PUNCT iajs-2703 8 4 𝑒 𝑒 NOUN iajs-2703 8 5 ) ) PUNCT iajs-2703 8 6 , , PUNCT iajs-2703 8 7 𝑒(𝑑0 𝑒(𝑑0 PROPN iajs-2703 8 8 ) ) PUNCT iajs-2703 8 9 = = SYM iajs-2703 8 10 𝑒0 𝑒0 PROPN iajs-2703 8 11 . . PUNCT iajs-2703 9 1 ( ( PUNCT iajs-2703 9 2 1 1 X iajs-2703 9 3 ) ) PUNCT iajs-2703 9 4 such such ADJ iajs-2703 9 5 problems problem NOUN iajs-2703 9 6 are be AUX iajs-2703 9 7 often often ADV iajs-2703 9 8 observed observe VERB iajs-2703 9 9 in in ADP iajs-2703 9 10 various various ADJ iajs-2703 9 11 applied apply VERB iajs-2703 9 12 sciences science NOUN iajs-2703 9 13 , , PUNCT iajs-2703 9 14 such such ADJ iajs-2703 9 15 as as ADP iajs-2703 9 16 quantum quantum ADJ iajs-2703 9 17 chemistry chemistry NOUN iajs-2703 9 18 , , PUNCT iajs-2703 9 19 astronomy astronomy NOUN iajs-2703 9 20 , , PUNCT iajs-2703 9 21 quantum quantum NOUN iajs-2703 9 22 mechanics mechanic NOUN iajs-2703 9 23 , , PUNCT iajs-2703 9 24 electronics electronic NOUN iajs-2703 9 25 , , PUNCT iajs-2703 9 26 elastics elastic NOUN iajs-2703 9 27 , , PUNCT iajs-2703 9 28 and and CCONJ iajs-2703 9 29 chemical chemical NOUN iajs-2703 9 30 physics physics NOUN iajs-2703 9 31 ( ( PUNCT iajs-2703 9 32 see see VERB iajs-2703 9 33 [ [ X iajs-2703 9 34 1,2 1,2 NUM iajs-2703 9 35 ] ] PUNCT iajs-2703 9 36 ) ) PUNCT iajs-2703 9 37 . . PUNCT iajs-2703 10 1 conventionally conventionally ADV iajs-2703 10 2 equation equation NOUN iajs-2703 10 3 ( ( PUNCT iajs-2703 10 4 1 1 X iajs-2703 10 5 ) ) PUNCT iajs-2703 10 6 is be AUX iajs-2703 10 7 solved solve VERB iajs-2703 10 8 by by ADP iajs-2703 10 9 using use VERB iajs-2703 10 10 runge runge NOUN iajs-2703 10 11 - - PUNCT iajs-2703 10 12 kutta kutta NOUN iajs-2703 10 13 ( ( PUNCT iajs-2703 10 14 rk rk NOUN iajs-2703 10 15 ) ) PUNCT iajs-2703 10 16 methods method NOUN iajs-2703 10 17 or or CCONJ iajs-2703 10 18 two two NUM iajs-2703 10 19 - - PUNCT iajs-2703 10 20 step step NOUN iajs-2703 10 21 methods method NOUN iajs-2703 10 22 [ [ X iajs-2703 10 23 3 3 NUM iajs-2703 10 24 ] ] PUNCT iajs-2703 10 25 . . PUNCT iajs-2703 11 1 several several ADJ iajs-2703 11 2 authors author NOUN iajs-2703 11 3 presented present VERB iajs-2703 11 4 optimized optimize VERB iajs-2703 11 5 numerical numerical ADJ iajs-2703 11 6 methods method NOUN iajs-2703 11 7 based base VERB iajs-2703 11 8 on on ADP iajs-2703 11 9 the the DET iajs-2703 11 10 phase phase NOUN iajs-2703 11 11 lag lag NOUN iajs-2703 11 12 characteristics characteristic NOUN iajs-2703 11 13 ( ( PUNCT iajs-2703 11 14 such such ADJ iajs-2703 11 15 as as ADP iajs-2703 11 16 [ [ X iajs-2703 11 17 4,5,6 4,5,6 NUM iajs-2703 11 18 ] ] NUM iajs-2703 11 19 ) ) PUNCT iajs-2703 11 20 . . PUNCT iajs-2703 12 1 exact exact ADJ iajs-2703 12 2 and and CCONJ iajs-2703 12 3 numerical numerical ADJ iajs-2703 12 4 solutions solution NOUN iajs-2703 12 5 produce produce VERB iajs-2703 12 6 an an DET iajs-2703 12 7 angle angle NOUN iajs-2703 12 8 between between ADP iajs-2703 12 9 them they PRON iajs-2703 12 10 is be AUX iajs-2703 12 11 known know VERB iajs-2703 12 12 as as ADP iajs-2703 12 13 phase phase NOUN iajs-2703 12 14 - - PUNCT iajs-2703 12 15 lag lag NOUN iajs-2703 12 16 , , PUNCT iajs-2703 12 17 and and CCONJ iajs-2703 12 18 the the DET iajs-2703 12 19 distance distance NOUN iajs-2703 12 20 of of ADP iajs-2703 12 21 the the DET iajs-2703 12 22 numerical numerical ADJ iajs-2703 12 23 solution solution NOUN iajs-2703 12 24 from from ADP iajs-2703 12 25 the the DET iajs-2703 12 26 periodic periodic ADJ iajs-2703 12 27 solution solution NOUN iajs-2703 12 28 is be AUX iajs-2703 12 29 called call VERB iajs-2703 12 30 amplification amplification NOUN iajs-2703 12 31 error error NOUN iajs-2703 12 32 . . PUNCT iajs-2703 13 1 a a DET iajs-2703 13 2 five five NUM iajs-2703 13 3 - - PUNCT iajs-2703 13 4 stage stage NOUN iajs-2703 13 5 four four NUM iajs-2703 13 6 order order NOUN iajs-2703 13 7 runge runge NOUN iajs-2703 13 8 - - PUNCT iajs-2703 13 9 kutta kutta NOUN iajs-2703 13 10 method method NOUN iajs-2703 13 11 with with ADP iajs-2703 13 12 phase phase NOUN iajs-2703 13 13 - - PUNCT iajs-2703 13 14 fitted fit VERB iajs-2703 13 15 and and CCONJ iajs-2703 13 16 amplification amplification NOUN iajs-2703 13 17 - - PUNCT iajs-2703 13 18 fitted fit VERB iajs-2703 13 19 proposed propose VERB iajs-2703 13 20 by by ADP iajs-2703 13 21 adel adel PROPN iajs-2703 13 22 et et PROPN iajs-2703 13 23 al al PROPN iajs-2703 13 24 . . PUNCT iajs-2703 14 1 [ [ X iajs-2703 14 2 7 7 NUM iajs-2703 14 3 ] ] PUNCT iajs-2703 14 4 . . PUNCT iajs-2703 15 1 hussain hussain PROPN iajs-2703 15 2 et et PROPN iajs-2703 15 3 al al PROPN iajs-2703 15 4 . . PUNCT iajs-2703 16 1 [ [ X iajs-2703 16 2 8 8 NUM iajs-2703 16 3 ] ] PUNCT iajs-2703 16 4 proposed propose VERB iajs-2703 16 5 an an DET iajs-2703 16 6 optimized optimize VERB iajs-2703 16 7 runge runge NOUN iajs-2703 16 8 - - PUNCT iajs-2703 16 9 kutta kutta NOUN iajs-2703 16 10 method method NOUN iajs-2703 16 11 to to PART iajs-2703 16 12 solve solve VERB iajs-2703 16 13 problem problem NOUN iajs-2703 16 14 ( ( PUNCT iajs-2703 16 15 1 1 NUM iajs-2703 16 16 ) ) PUNCT iajs-2703 16 17 . . PUNCT iajs-2703 17 1 the the DET iajs-2703 17 2 phase phase NOUN iajs-2703 17 3 lag lag NOUN iajs-2703 17 4 has have VERB iajs-2703 17 5 the the DET iajs-2703 17 6 feature feature NOUN iajs-2703 17 7 to to PART iajs-2703 17 8 develop develop VERB iajs-2703 17 9 more more ADV iajs-2703 17 10 accurate accurate ADJ iajs-2703 17 11 numerical numerical ADJ iajs-2703 17 12 methods method NOUN iajs-2703 17 13 . . PUNCT iajs-2703 18 1 this this PRON iajs-2703 18 2 motivates motivate VERB iajs-2703 18 3 us we PRON iajs-2703 18 4 to to PART iajs-2703 18 5 propose propose VERB iajs-2703 18 6 the the DET iajs-2703 18 7 runge runge NOUN iajs-2703 18 8 - - PUNCT iajs-2703 18 9 kutta kutta NOUN iajs-2703 18 10 ibn ibn PROPN iajs-2703 18 11 al al PROPN iajs-2703 18 12 haitham haitham PROPN iajs-2703 18 13 journal journal PROPN iajs-2703 18 14 for for ADP iajs-2703 18 15 pure pure ADJ iajs-2703 18 16 and and CCONJ iajs-2703 18 17 applied apply VERB iajs-2703 18 18 science science NOUN iajs-2703 18 19 journal journal PROPN iajs-2703 18 20 homepage homepage NOUN iajs-2703 18 21 : : PUNCT iajs-2703 18 22 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index NOUN iajs-2703 18 23 doi doi NOUN iajs-2703 18 24 : : PUNCT iajs-2703 18 25 10.30526/34.4.2703 10.30526/34.4.2703 PROPN iajs-2703 18 26 article article NOUN iajs-2703 18 27 history history NOUN iajs-2703 18 28 : : PUNCT iajs-2703 18 29 received receive VERB iajs-2703 18 30 11 11 NUM iajs-2703 18 31 april april PROPN iajs-2703 18 32 2021 2021 NUM iajs-2703 18 33 , , PUNCT iajs-2703 18 34 accepted accept VERB iajs-2703 18 35 30 30 NUM iajs-2703 18 36 may may NOUN iajs-2703 18 37 2021 2021 NUM iajs-2703 18 38 , , PUNCT iajs-2703 18 39 published publish VERB iajs-2703 18 40 in in ADP iajs-2703 18 41 october october PROPN iajs-2703 18 42 2021 2021 NUM iajs-2703 18 43 . . PUNCT iajs-2703 19 1 mailto:kasimabbas@uomustansiriyah.edu.iq mailto:kasimabbas@uomustansiriyah.edu.iq NOUN iajs-2703 19 2 % % PROPN iajs-2703 19 3 20zkgzainab@gmail.com 20zkgzainab@gmail.com PROPN iajs-2703 19 4 ibn ibn PROPN iajs-2703 19 5 al al PROPN iajs-2703 19 6 - - PUNCT iajs-2703 19 7 haitham haitham PROPN iajs-2703 19 8 jour jour X iajs-2703 19 9 . . PROPN iajs-2703 19 10 for for ADP iajs-2703 19 11 pure pure ADJ iajs-2703 19 12 & & CCONJ iajs-2703 19 13 appl appl PROPN iajs-2703 19 14 . . PUNCT iajs-2703 20 1 sci sci PROPN iajs-2703 20 2 . . PROPN iajs-2703 21 1 34(4)2021 34(4)2021 NUM iajs-2703 21 2 59 59 NUM iajs-2703 21 3 methods method NOUN iajs-2703 21 4 by by ADP iajs-2703 21 5 using use VERB iajs-2703 21 6 phase phase NOUN iajs-2703 21 7 lag lag NOUN iajs-2703 21 8 properties property NOUN iajs-2703 21 9 . . PUNCT iajs-2703 22 1 based base VERB iajs-2703 22 2 on on ADP iajs-2703 22 3 the the DET iajs-2703 22 4 previous previous ADJ iajs-2703 22 5 work work NOUN iajs-2703 22 6 , , PUNCT iajs-2703 22 7 we we PRON iajs-2703 22 8 present present VERB iajs-2703 22 9 a a DET iajs-2703 22 10 modified modified ADJ iajs-2703 22 11 approach approach NOUN iajs-2703 22 12 for for ADP iajs-2703 22 13 the the DET iajs-2703 22 14 runge runge NOUN iajs-2703 22 15 – – PUNCT iajs-2703 22 16 kutta kutta NOUN iajs-2703 22 17 methods method NOUN iajs-2703 22 18 by by ADP iajs-2703 22 19 combining combine VERB iajs-2703 22 20 the the DET iajs-2703 22 21 annulment annulment NOUN iajs-2703 22 22 of of ADP iajs-2703 22 23 phase phase NOUN iajs-2703 22 24 lag lag NOUN iajs-2703 22 25 , , PUNCT iajs-2703 22 26 phase phase NOUN iajs-2703 22 27 lag lag NOUN iajs-2703 22 28 's 's PART iajs-2703 22 29 derivative derivative NOUN iajs-2703 22 30 , , PUNCT iajs-2703 22 31 and and CCONJ iajs-2703 22 32 amplification amplification NOUN iajs-2703 22 33 factor factor NOUN iajs-2703 22 34 . . PUNCT iajs-2703 23 1 the the DET iajs-2703 23 2 new new ADJ iajs-2703 23 3 mrk mrk PROPN iajs-2703 23 4 methods method NOUN iajs-2703 23 5 have have AUX iajs-2703 23 6 been be AUX iajs-2703 23 7 used use VERB iajs-2703 23 8 to to PART iajs-2703 23 9 solve solve VERB iajs-2703 23 10 oscillation oscillation NOUN iajs-2703 23 11 problems problem NOUN iajs-2703 23 12 . . PUNCT iajs-2703 24 1 the the DET iajs-2703 24 2 paper paper NOUN iajs-2703 24 3 is be AUX iajs-2703 24 4 orderly orderly ADJ iajs-2703 24 5 as as SCONJ iajs-2703 24 6 follows follow VERB iajs-2703 24 7 : : PUNCT iajs-2703 24 8 in in ADP iajs-2703 24 9 section section NOUN iajs-2703 24 10 2 2 NUM iajs-2703 24 11 , , PUNCT iajs-2703 24 12 the the DET iajs-2703 24 13 phase phase NOUN iajs-2703 24 14 - - PUNCT iajs-2703 24 15 lag lag NOUN iajs-2703 24 16 properties property NOUN iajs-2703 24 17 of of ADP iajs-2703 24 18 the the DET iajs-2703 24 19 mrk mrk PROPN iajs-2703 24 20 method method NOUN iajs-2703 24 21 are be AUX iajs-2703 24 22 given give VERB iajs-2703 24 23 . . PUNCT iajs-2703 25 1 in in ADP iajs-2703 25 2 section section NOUN iajs-2703 25 3 3 3 NUM iajs-2703 25 4 , , PUNCT iajs-2703 25 5 we we PRON iajs-2703 25 6 present present VERB iajs-2703 25 7 how how SCONJ iajs-2703 25 8 the the DET iajs-2703 25 9 new new ADJ iajs-2703 25 10 methods method NOUN iajs-2703 25 11 are be AUX iajs-2703 25 12 derived derive VERB iajs-2703 25 13 . . PUNCT iajs-2703 26 1 in in ADP iajs-2703 26 2 section section NOUN iajs-2703 26 3 4 4 NUM iajs-2703 26 4 , , PUNCT iajs-2703 26 5 we we PRON iajs-2703 26 6 offer offer VERB iajs-2703 26 7 numerical numerical ADJ iajs-2703 26 8 results result NOUN iajs-2703 26 9 to to PART iajs-2703 26 10 illustrate illustrate VERB iajs-2703 26 11 the the DET iajs-2703 26 12 efficiency efficiency NOUN iajs-2703 26 13 of of ADP iajs-2703 26 14 the the DET iajs-2703 26 15 new new ADJ iajs-2703 26 16 mrk mrk PROPN iajs-2703 26 17 method method NOUN iajs-2703 26 18 . . PUNCT iajs-2703 27 1 section section NOUN iajs-2703 27 2 5 5 NUM iajs-2703 27 3 is be AUX iajs-2703 27 4 dedicated dedicate VERB iajs-2703 27 5 to to ADP iajs-2703 27 6 conclusions conclusion NOUN iajs-2703 27 7 . . PUNCT iajs-2703 28 1 2 2 X iajs-2703 28 2 . . NOUN iajs-2703 28 3 phase phase NOUN iajs-2703 28 4 lag lag NOUN iajs-2703 28 5 properties property NOUN iajs-2703 28 6 of of ADP iajs-2703 28 7 mrk mrk PROPN iajs-2703 28 8 methods method NOUN iajs-2703 28 9 we we PRON iajs-2703 28 10 are be AUX iajs-2703 28 11 concerned concerned ADJ iajs-2703 28 12 with with ADP iajs-2703 28 13 the the DET iajs-2703 28 14 numerical numerical ADJ iajs-2703 28 15 solution solution NOUN iajs-2703 28 16 of of ADP iajs-2703 28 17 the the DET iajs-2703 28 18 odes ode NOUN iajs-2703 28 19 of of ADP iajs-2703 28 20 the the DET iajs-2703 28 21 form form NOUN iajs-2703 28 22 ( ( PUNCT iajs-2703 28 23 1 1 NUM iajs-2703 28 24 ) ) PUNCT iajs-2703 28 25 with with ADP iajs-2703 28 26 an an DET iajs-2703 28 27 oscillating oscillate VERB iajs-2703 28 28 solution solution NOUN iajs-2703 28 29 . . PUNCT iajs-2703 29 1 the the DET iajs-2703 29 2 general general ADJ iajs-2703 29 3 form form NOUN iajs-2703 29 4 of of ADP iajs-2703 29 5 explicit explicit ADJ iajs-2703 29 6 mrk mrk NOUN iajs-2703 29 7 method method NOUN iajs-2703 29 8 for for ADP iajs-2703 29 9 solving solve VERB iajs-2703 29 10 ( ( PUNCT iajs-2703 29 11 1 1 NUM iajs-2703 29 12 ) ) PUNCT iajs-2703 29 13 is be AUX iajs-2703 29 14 defined define VERB iajs-2703 29 15 as as SCONJ iajs-2703 29 16 follows follow VERB iajs-2703 29 17 : : PUNCT iajs-2703 29 18 𝑒𝑛+1 𝑒𝑛+1 NUM iajs-2703 29 19 = = SYM iajs-2703 29 20 𝑒𝑛 𝑒𝑛 NOUN iajs-2703 29 21 + + PROPN iajs-2703 29 22 βˆ‘ βˆ‘ PROPN iajs-2703 29 23 𝑏𝑖𝑓(𝑑𝑛 𝑏𝑖𝑓(𝑑𝑛 ADJ iajs-2703 29 24 + + CCONJ iajs-2703 29 25 𝑐𝑖 𝑐𝑖 NOUN iajs-2703 29 26 , , PUNCT iajs-2703 29 27 π‘ˆπ‘– π‘ˆπ‘– PROPN iajs-2703 29 28 ) ) PUNCT iajs-2703 29 29 𝑠 𝑠 PROPN iajs-2703 29 30 𝑖=1 𝑖=1 PROPN iajs-2703 29 31 ( ( PUNCT iajs-2703 29 32 2 2 X iajs-2703 29 33 ) ) PUNCT iajs-2703 29 34 π‘ˆπ‘– π‘ˆπ‘– NOUN iajs-2703 29 35 = = PUNCT iajs-2703 29 36 𝑑𝑖𝑒𝑛 𝑑𝑖𝑒𝑛 NOUN iajs-2703 29 37 + + CCONJ iajs-2703 29 38 β„Ž β„Ž X iajs-2703 29 39 βˆ‘ βˆ‘ PROPN iajs-2703 29 40 π‘Žπ‘–π‘— π‘Žπ‘–π‘— NOUN iajs-2703 29 41 π‘–βˆ’1 π‘–βˆ’1 PUNCT iajs-2703 29 42 𝑗=1 𝑗=1 PROPN iajs-2703 29 43 𝑓(𝑑𝑛 𝑓(𝑑𝑛 ADJ iajs-2703 29 44 + + CCONJ iajs-2703 29 45 π‘π‘–β„Ž π‘π‘–β„Ž ADJ iajs-2703 29 46 , , PUNCT iajs-2703 29 47 π‘ˆπ‘— π‘ˆπ‘— PROPN iajs-2703 29 48 ) ) PUNCT iajs-2703 29 49 , , PUNCT iajs-2703 29 50 𝑖 𝑖 NOUN iajs-2703 29 51 = = SYM iajs-2703 29 52 1,2 1,2 NUM iajs-2703 29 53 , , PUNCT iajs-2703 29 54 . . PUNCT iajs-2703 29 55 . . PUNCT iajs-2703 30 1 . . PUNCT iajs-2703 31 1 , , PUNCT iajs-2703 31 2 𝑠. 𝑠. NOUN iajs-2703 31 3 ( ( PUNCT iajs-2703 31 4 3 3 X iajs-2703 31 5 ) ) PUNCT iajs-2703 31 6 the the DET iajs-2703 31 7 corresponding corresponding ADJ iajs-2703 31 8 butcher butcher NOUN iajs-2703 31 9 tableau tableau PROPN iajs-2703 31 10 for for ADP iajs-2703 31 11 equations equation NOUN iajs-2703 31 12 ( ( PUNCT iajs-2703 31 13 2 2 NUM iajs-2703 31 14 ) ) PUNCT iajs-2703 31 15 – – PUNCT iajs-2703 31 16 ( ( PUNCT iajs-2703 31 17 3 3 X iajs-2703 31 18 ) ) PUNCT iajs-2703 31 19 is be AUX iajs-2703 31 20 expressed express VERB iajs-2703 31 21 as as SCONJ iajs-2703 31 22 follows follow VERB iajs-2703 31 23 table table NOUN iajs-2703 31 24 1 1 NUM iajs-2703 31 25 . . PUNCT iajs-2703 32 1 s s X iajs-2703 32 2 - - PUNCT iajs-2703 32 3 stage stage NOUN iajs-2703 32 4 modified modify VERB iajs-2703 32 5 mrk mrk PROPN iajs-2703 32 6 method method NOUN iajs-2703 32 7 0 0 NUM iajs-2703 32 8 𝑐2 𝑐2 NOUN iajs-2703 32 9 𝑑2 𝑑2 NOUN iajs-2703 32 10 π‘Ž21 π‘Ž21 NOUN iajs-2703 32 11 𝑐3 𝑐3 NOUN iajs-2703 32 12 𝑑3 𝑑3 PROPN iajs-2703 32 13 π‘Ž31 π‘Ž31 NOUN iajs-2703 32 14 π‘Ž32 π‘Ž32 NOUN iajs-2703 32 15 . . PUNCT iajs-2703 32 16 . . PUNCT iajs-2703 32 17 . . PUNCT iajs-2703 32 18 . . PUNCT iajs-2703 32 19 . . PUNCT iajs-2703 32 20 . . PUNCT iajs-2703 32 21 . . PUNCT iajs-2703 32 22 . . PUNCT iajs-2703 32 23 . . PUNCT iajs-2703 32 24 . . PUNCT iajs-2703 32 25 . . PUNCT iajs-2703 32 26 . . PUNCT iajs-2703 32 27 . . PUNCT iajs-2703 33 1 . . PUNCT iajs-2703 34 1 . . PUNCT iajs-2703 35 1 𝑐𝑠 𝑐𝑠 VERB iajs-2703 35 2 𝑑𝑠 𝑑𝑠 ADP iajs-2703 35 3 π‘Žπ‘ 1 π‘Žπ‘ 1 PRON iajs-2703 35 4 π‘Žπ‘ 2 π‘Žπ‘ 2 NOUN iajs-2703 35 5 … … PUNCT iajs-2703 35 6 π‘Žπ‘ π‘ βˆ’1 π‘Žπ‘ π‘ βˆ’1 ADJ iajs-2703 35 7 𝑏1 𝑏1 ADJ iajs-2703 35 8 𝑏2 𝑏2 NOUN iajs-2703 35 9 … … PUNCT iajs-2703 35 10 π‘π‘ π‘ βˆ’1 π‘π‘ π‘ βˆ’1 PROPN iajs-2703 35 11 𝑏𝑠 𝑏𝑠 NOUN iajs-2703 35 12 constructing construct VERB iajs-2703 35 13 the the DET iajs-2703 35 14 new new ADJ iajs-2703 35 15 method method NOUN iajs-2703 35 16 depends depend VERB iajs-2703 35 17 on on ADP iajs-2703 35 18 phase phase NOUN iajs-2703 35 19 - - PUNCT iajs-2703 35 20 lag lag NOUN iajs-2703 35 21 and and CCONJ iajs-2703 35 22 dissipation dissipation NOUN iajs-2703 35 23 analysis analysis NOUN iajs-2703 35 24 proposed propose VERB iajs-2703 35 25 in in ADP iajs-2703 35 26 [ [ X iajs-2703 35 27 9 9 NUM iajs-2703 35 28 ] ] PUNCT iajs-2703 35 29 . . PUNCT iajs-2703 36 1 to to ADP iajs-2703 36 2 this this DET iajs-2703 36 3 goal goal NOUN iajs-2703 36 4 , , PUNCT iajs-2703 36 5 we we PRON iajs-2703 36 6 use use VERB iajs-2703 36 7 the the DET iajs-2703 36 8 following follow VERB iajs-2703 36 9 test test NOUN iajs-2703 36 10 equation equation NOUN iajs-2703 36 11 , , PUNCT iajs-2703 36 12 𝑒′ 𝑒′ ADJ iajs-2703 36 13 = = SYM iajs-2703 36 14 𝑖𝑀𝑒 𝑖𝑀𝑒 PROPN iajs-2703 36 15 , , PUNCT iajs-2703 36 16 𝑀 𝑀 ADP iajs-2703 36 17 ∈ ∈ PROPN iajs-2703 36 18 𝑅 𝑅 PROPN iajs-2703 36 19 ( ( PUNCT iajs-2703 36 20 4 4 NUM iajs-2703 36 21 ) ) PUNCT iajs-2703 36 22 an an DET iajs-2703 36 23 implementation implementation NOUN iajs-2703 36 24 of of ADP iajs-2703 36 25 mrk mrk PROPN iajs-2703 36 26 method method NOUN iajs-2703 36 27 ( ( PUNCT iajs-2703 36 28 2)-(3 2)-(3 NUM iajs-2703 36 29 ) ) PUNCT iajs-2703 36 30 to to ADP iajs-2703 36 31 the the DET iajs-2703 36 32 test test NOUN iajs-2703 36 33 equation equation NOUN iajs-2703 36 34 ( ( PUNCT iajs-2703 36 35 4 4 X iajs-2703 36 36 ) ) PUNCT iajs-2703 36 37 we we PRON iajs-2703 36 38 yield yield VERB iajs-2703 36 39 𝑒𝑛 𝑒𝑛 NOUN iajs-2703 36 40 = = PUNCT iajs-2703 36 41 π‘žβˆ— π‘žβˆ— PROPN iajs-2703 36 42 𝑛 𝑛 PRON iajs-2703 36 43 𝑒0 𝑒0 PROPN iajs-2703 36 44 , , PUNCT iajs-2703 36 45 π‘žβˆ— π‘žβˆ— PROPN iajs-2703 36 46 𝑛 𝑛 NOUN iajs-2703 36 47 = = SYM iajs-2703 36 48 𝑆(𝑧2 𝑆(𝑧2 PROPN iajs-2703 36 49 ) ) PUNCT iajs-2703 37 1 + + CCONJ iajs-2703 37 2 𝑖𝑧 𝑖𝑧 ADP iajs-2703 37 3 𝑉(𝑧2 𝑉(𝑧2 NOUN iajs-2703 37 4 ) ) PUNCT iajs-2703 37 5 ( ( PUNCT iajs-2703 37 6 5 5 NUM iajs-2703 37 7 ) ) PUNCT iajs-2703 37 8 where where SCONJ iajs-2703 37 9 𝑧 𝑧 NOUN iajs-2703 37 10 = = X iajs-2703 37 11 π‘€β„Ž π‘€β„Ž X iajs-2703 37 12 and and CCONJ iajs-2703 37 13 𝑆 𝑆 PROPN iajs-2703 37 14 , , PUNCT iajs-2703 37 15 𝑉 𝑉 PROPN iajs-2703 37 16 are be AUX iajs-2703 37 17 polynomials polynomial NOUN iajs-2703 37 18 in in ADP iajs-2703 37 19 𝑧2 𝑧2 NOUN iajs-2703 37 20 entirely entirely ADV iajs-2703 37 21 specified specify VERB iajs-2703 37 22 by by ADP iajs-2703 37 23 the the DET iajs-2703 37 24 coefficients coefficient NOUN iajs-2703 37 25 π‘Žπ‘–π‘— π‘Žπ‘–π‘— NOUN iajs-2703 37 26 , , PUNCT iajs-2703 37 27 𝑐𝑖 𝑐𝑖 NOUN iajs-2703 37 28 and and CCONJ iajs-2703 37 29 𝑏𝑖 𝑏𝑖 ADP iajs-2703 37 30 of of ADP iajs-2703 37 31 mrk mrk PROPN iajs-2703 37 32 method method NOUN iajs-2703 37 33 ( ( PUNCT iajs-2703 37 34 2)-(3 2)-(3 NUM iajs-2703 37 35 ) ) PUNCT iajs-2703 37 36 . . PUNCT iajs-2703 38 1 the the DET iajs-2703 38 2 comparison comparison NOUN iajs-2703 38 3 between between ADP iajs-2703 38 4 equations equation NOUN iajs-2703 38 5 ( ( PUNCT iajs-2703 38 6 5 5 NUM iajs-2703 38 7 ) ) PUNCT iajs-2703 38 8 and and CCONJ iajs-2703 38 9 ( ( PUNCT iajs-2703 38 10 4 4 X iajs-2703 38 11 ) ) PUNCT iajs-2703 38 12 produces produce VERB iajs-2703 38 13 the the DET iajs-2703 38 14 following follow VERB iajs-2703 38 15 definition definition NOUN iajs-2703 38 16 . . PUNCT iajs-2703 39 1 definition definition NOUN iajs-2703 39 2 : : PUNCT iajs-2703 40 1 [ [ X iajs-2703 40 2 9 9 X iajs-2703 40 3 ] ] X iajs-2703 40 4 the the DET iajs-2703 40 5 following follow VERB iajs-2703 40 6 quantities quantity NOUN iajs-2703 40 7 in in ADP iajs-2703 40 8 rk rk NOUN iajs-2703 40 9 method method NOUN iajs-2703 40 10 ( ( PUNCT iajs-2703 40 11 2)-(3 2)-(3 NUM iajs-2703 40 12 ) ) PUNCT iajs-2703 40 13 1𝑃(𝑧 1𝑃(𝑧 X iajs-2703 40 14 ) ) PUNCT iajs-2703 41 1 = = PUNCT iajs-2703 41 2 𝑧 𝑧 PRON iajs-2703 41 3 βˆ’ βˆ’ NOUN iajs-2703 41 4 arg[π‘žβˆ—(𝑧 arg[π‘žβˆ—(𝑧 PROPN iajs-2703 41 5 ) ) PUNCT iajs-2703 41 6 ] ] PUNCT iajs-2703 42 1 = = PUNCT iajs-2703 42 2 𝑧 𝑧 PRON iajs-2703 42 3 βˆ’ βˆ’ PROPN iajs-2703 42 4 tanβˆ’1 tanβˆ’1 PROPN iajs-2703 42 5 ( ( PUNCT iajs-2703 42 6 𝑧.𝑉(𝑧2 𝑧.𝑉(𝑧2 ADJ iajs-2703 42 7 ) ) PUNCT iajs-2703 42 8 𝑆(𝑧2 𝑆(𝑧2 NOUN iajs-2703 42 9 ) ) PUNCT iajs-2703 42 10 ) ) PUNCT iajs-2703 42 11 , , PUNCT iajs-2703 43 1 2𝐷(𝑧 2𝐷(𝑧 X iajs-2703 43 2 ) ) PUNCT iajs-2703 43 3 = = SYM iajs-2703 43 4 1 1 NUM iajs-2703 43 5 βˆ’ βˆ’ NOUN iajs-2703 43 6 |π‘žβˆ—(𝑧)| |π‘žβˆ—(𝑧)| VERB iajs-2703 43 7 = = SYM iajs-2703 43 8 1 1 NUM iajs-2703 43 9 βˆ’ βˆ’ NOUN iajs-2703 43 10 √(𝑆2(𝑧2 √(𝑆2(𝑧2 NOUN iajs-2703 43 11 ) ) PUNCT iajs-2703 43 12 + + CCONJ iajs-2703 43 13 𝑧2 𝑧2 PROPN iajs-2703 43 14 𝑉2(𝑧2 𝑉2(𝑧2 PROPN iajs-2703 43 15 ) ) PUNCT iajs-2703 43 16 ) ) PUNCT iajs-2703 43 17 . . PUNCT iajs-2703 44 1 are be AUX iajs-2703 44 2 respectively respectively ADV iajs-2703 44 3 called call VERB iajs-2703 44 4 phase phase NOUN iajs-2703 44 5 lag lag NOUN iajs-2703 44 6 or or CCONJ iajs-2703 44 7 dispersion dispersion NOUN iajs-2703 44 8 error error NOUN iajs-2703 44 9 and and CCONJ iajs-2703 44 10 the the DET iajs-2703 44 11 amplification amplification NOUN iajs-2703 44 12 factor factor NOUN iajs-2703 44 13 or or CCONJ iajs-2703 44 14 dissipation dissipation NOUN iajs-2703 44 15 error error NOUN iajs-2703 44 16 . . PUNCT iajs-2703 45 1 if if SCONJ iajs-2703 45 2 𝑃(𝑧 𝑃(𝑧 PRON iajs-2703 45 3 ) ) PUNCT iajs-2703 45 4 = = SYM iajs-2703 45 5 ΞΏ(π‘§π‘Ÿ+1 ΞΏ(π‘§π‘Ÿ+1 NOUN iajs-2703 45 6 ) ) PUNCT iajs-2703 45 7 and and CCONJ iajs-2703 45 8 𝐷(𝑧 𝐷(𝑧 X iajs-2703 45 9 ) ) PUNCT iajs-2703 45 10 = = SYM iajs-2703 45 11 ΞΏ(𝑧𝑝+1 ΞΏ(𝑧𝑝+1 NOUN iajs-2703 45 12 ) ) PUNCT iajs-2703 45 13 , , PUNCT iajs-2703 45 14 then then ADV iajs-2703 45 15 the the DET iajs-2703 45 16 method method NOUN iajs-2703 45 17 is be AUX iajs-2703 45 18 said say VERB iajs-2703 45 19 to to PART iajs-2703 45 20 be be AUX iajs-2703 45 21 of of ADP iajs-2703 45 22 dispersion dispersion NOUN iajs-2703 45 23 order order NOUN iajs-2703 45 24 π‘Ÿ π‘Ÿ NOUN iajs-2703 45 25 and and CCONJ iajs-2703 45 26 dissipation dissipation NOUN iajs-2703 45 27 order order NOUN iajs-2703 45 28 𝑝 𝑝 NOUN iajs-2703 45 29 . . PUNCT iajs-2703 46 1 3 3 X iajs-2703 46 2 . . X iajs-2703 46 3 derivation derivation NOUN iajs-2703 46 4 of of ADP iajs-2703 46 5 new new ADJ iajs-2703 46 6 mrk mrk PROPN iajs-2703 46 7 methods method NOUN iajs-2703 46 8 this this DET iajs-2703 46 9 section section NOUN iajs-2703 46 10 proceeds proceed VERB iajs-2703 46 11 to to PART iajs-2703 46 12 derive derive VERB iajs-2703 46 13 the the DET iajs-2703 46 14 modified modify VERB iajs-2703 46 15 rk rk NOUN iajs-2703 46 16 method method NOUN iajs-2703 46 17 by by ADP iajs-2703 46 18 abolishing abolish VERB iajs-2703 46 19 phase phase NOUN iajs-2703 46 20 lag lag NOUN iajs-2703 46 21 , , PUNCT iajs-2703 46 22 phase phase NOUN iajs-2703 46 23 lag lag NOUN iajs-2703 46 24 ’s ’s PART iajs-2703 46 25 derivative derivative ADJ iajs-2703 46 26 , , PUNCT iajs-2703 46 27 and and CCONJ iajs-2703 46 28 amplification amplification NOUN iajs-2703 46 29 error error NOUN iajs-2703 46 30 . . PUNCT iajs-2703 47 1 ibn ibn PROPN iajs-2703 47 2 al al PROPN iajs-2703 47 3 - - PUNCT iajs-2703 47 4 haitham haitham PROPN iajs-2703 47 5 jour jour X iajs-2703 47 6 . . PROPN iajs-2703 47 7 for for ADP iajs-2703 47 8 pure pure ADJ iajs-2703 47 9 & & CCONJ iajs-2703 47 10 appl appl PROPN iajs-2703 47 11 . . PUNCT iajs-2703 48 1 sci sci PROPN iajs-2703 48 2 . . PROPN iajs-2703 49 1 34(4)2021 34(4)2021 NUM iajs-2703 49 2 60 60 NUM iajs-2703 49 3 3.1 3.1 NUM iajs-2703 49 4 five five NUM iajs-2703 49 5 - - PUNCT iajs-2703 49 6 stage stage NOUN iajs-2703 49 7 fourth fourth ADJ iajs-2703 49 8 - - PUNCT iajs-2703 49 9 order order NOUN iajs-2703 49 10 method method NOUN iajs-2703 49 11 a a DET iajs-2703 49 12 fourth fourth ADJ iajs-2703 49 13 - - PUNCT iajs-2703 49 14 order order NOUN iajs-2703 49 15 mrk mrk NOUN iajs-2703 49 16 method method NOUN iajs-2703 49 17 of of ADP iajs-2703 49 18 five five NUM iajs-2703 49 19 - - PUNCT iajs-2703 49 20 stage stage NOUN iajs-2703 49 21 is be AUX iajs-2703 49 22 given give VERB iajs-2703 49 23 as as SCONJ iajs-2703 49 24 follows follow VERB iajs-2703 49 25 [ [ X iajs-2703 49 26 10 10 NUM iajs-2703 49 27 ] ] NUM iajs-2703 49 28 : : PUNCT iajs-2703 49 29 table table NOUN iajs-2703 49 30 2 2 NUM iajs-2703 49 31 . . NUM iajs-2703 49 32 five five NUM iajs-2703 49 33 - - PUNCT iajs-2703 49 34 stage stage NOUN iajs-2703 49 35 modified modify VERB iajs-2703 49 36 explicit explicit ADJ iajs-2703 49 37 runge runge NOUN iajs-2703 49 38 - - PUNCT iajs-2703 49 39 kutta kutta NOUN iajs-2703 49 40 method method NOUN iajs-2703 49 41 to to PART iajs-2703 49 42 construct construct VERB iajs-2703 49 43 a a DET iajs-2703 49 44 modified modify VERB iajs-2703 49 45 rk rk NOUN iajs-2703 49 46 method method NOUN iajs-2703 49 47 , , PUNCT iajs-2703 49 48 we we PRON iajs-2703 49 49 set set VERB iajs-2703 49 50 𝑑2 𝑑2 NOUN iajs-2703 49 51 , , PUNCT iajs-2703 49 52 𝑑3 𝑑3 NOUN iajs-2703 49 53 , , PUNCT iajs-2703 49 54 and and CCONJ iajs-2703 49 55 𝑑4 𝑑4 ADV iajs-2703 49 56 as as SCONJ iajs-2703 49 57 free free ADJ iajs-2703 49 58 parameters parameter NOUN iajs-2703 49 59 and and CCONJ iajs-2703 49 60 the the DET iajs-2703 49 61 other other ADJ iajs-2703 49 62 parameters parameter NOUN iajs-2703 49 63 are be AUX iajs-2703 49 64 the the DET iajs-2703 49 65 same same ADJ iajs-2703 49 66 as as ADP iajs-2703 49 67 in in ADP iajs-2703 49 68 table table NOUN iajs-2703 49 69 2 2 NUM iajs-2703 49 70 . . NUM iajs-2703 49 71 motivated motivate VERB iajs-2703 49 72 by by ADP iajs-2703 49 73 the the DET iajs-2703 49 74 approach approach NOUN iajs-2703 49 75 in in ADP iajs-2703 49 76 [ [ X iajs-2703 49 77 8 8 NUM iajs-2703 49 78 ] ] PUNCT iajs-2703 49 79 , , PUNCT iajs-2703 49 80 we we PRON iajs-2703 49 81 obtain obtain VERB iajs-2703 49 82 the the DET iajs-2703 49 83 phase phase NOUN iajs-2703 49 84 lag lag NOUN iajs-2703 49 85 , , PUNCT iajs-2703 49 86 phase phase NOUN iajs-2703 49 87 lag lag NOUN iajs-2703 49 88 derivative derivative NOUN iajs-2703 49 89 and and CCONJ iajs-2703 49 90 the the DET iajs-2703 49 91 amplification amplification NOUN iajs-2703 49 92 factor factor NOUN iajs-2703 49 93 , , PUNCT iajs-2703 49 94 which which PRON iajs-2703 49 95 depend depend VERB iajs-2703 49 96 on on ADP iajs-2703 49 97 𝑑2 𝑑2 NOUN iajs-2703 49 98 , , PUNCT iajs-2703 49 99 𝑑3 𝑑3 NOUN iajs-2703 49 100 and and CCONJ iajs-2703 49 101 𝑑4 𝑑4 ADV iajs-2703 49 102 as as SCONJ iajs-2703 49 103 follow follow VERB iajs-2703 49 104 : : PUNCT iajs-2703 49 105 𝑃(𝑧 𝑃(𝑧 X iajs-2703 49 106 ) ) PUNCT iajs-2703 49 107 = = SYM iajs-2703 49 108 tan(𝑧 tan(𝑧 PROPN iajs-2703 49 109 ) ) PUNCT iajs-2703 49 110 ( ( PUNCT iajs-2703 49 111 1 1 NUM iajs-2703 49 112 24 24 NUM iajs-2703 49 113 𝑑2 𝑑2 NOUN iajs-2703 49 114 𝑧4 𝑧4 PROPN iajs-2703 49 115 + + CCONJ iajs-2703 49 116 ( ( PUNCT iajs-2703 49 117 βˆ’ βˆ’ PROPN iajs-2703 49 118 5 5 NUM iajs-2703 49 119 16 16 NUM iajs-2703 49 120 𝑑3 𝑑3 NOUN iajs-2703 49 121 βˆ’ βˆ’ PROPN iajs-2703 49 122 5 5 NUM iajs-2703 49 123 96 96 NUM iajs-2703 49 124 𝑑4 𝑑4 ADV iajs-2703 49 125 βˆ’ βˆ’ PROPN iajs-2703 49 126 13 13 NUM iajs-2703 49 127 96 96 NUM iajs-2703 49 128 ) ) PUNCT iajs-2703 49 129 𝑧2 𝑧2 NOUN iajs-2703 50 1 + + CCONJ iajs-2703 50 2 1 1 NUM iajs-2703 50 3 ) ) PUNCT iajs-2703 50 4 βˆ’ βˆ’ PROPN iajs-2703 51 1 𝑧 𝑧 PROPN iajs-2703 51 2 ( ( PUNCT iajs-2703 51 3 1 1 NUM iajs-2703 51 4 120 120 NUM iajs-2703 51 5 𝑧4 𝑧4 NOUN iajs-2703 51 6 + + CCONJ iajs-2703 51 7 ( ( PUNCT iajs-2703 51 8 βˆ’ βˆ’ PROPN iajs-2703 51 9 1 1 NUM iajs-2703 51 10 16 16 NUM iajs-2703 51 11 βˆ’ βˆ’ NUM iajs-2703 51 12 5 5 NUM iajs-2703 51 13 48 48 NUM iajs-2703 51 14 𝑑3 𝑑3 NOUN iajs-2703 51 15 ) ) PUNCT iajs-2703 51 16 𝑧2 𝑧2 NOUN iajs-2703 52 1 + + CCONJ iajs-2703 52 2 7 7 NUM iajs-2703 52 3 32 32 NUM iajs-2703 52 4 + + CCONJ iajs-2703 52 5 25 25 NUM iajs-2703 52 6 48 48 NUM iajs-2703 52 7 𝑑3 𝑑3 NOUN iajs-2703 52 8 + + CCONJ iajs-2703 52 9 25 25 NUM iajs-2703 52 10 96 96 NUM iajs-2703 52 11 𝑑4 𝑑4 ADJ iajs-2703 52 12 ) ) PUNCT iajs-2703 52 13 , , PUNCT iajs-2703 52 14 ( ( PUNCT iajs-2703 52 15 6 6 X iajs-2703 52 16 ) ) PUNCT iajs-2703 52 17 𝑃′(𝑧 𝑃′(𝑧 PROPN iajs-2703 52 18 ) ) PUNCT iajs-2703 52 19 = = PUNCT iajs-2703 53 1 ( ( PUNCT iajs-2703 53 2 1 1 NUM iajs-2703 53 3 + + NUM iajs-2703 53 4 π‘‘π‘Žπ‘›2(𝑧 π‘‘π‘Žπ‘›2(𝑧 NOUN iajs-2703 53 5 ) ) PUNCT iajs-2703 53 6 ) ) PUNCT iajs-2703 54 1 ( ( PUNCT iajs-2703 54 2 1 1 NUM iajs-2703 54 3 24 24 NUM iajs-2703 54 4 𝑑2𝑧4 𝑑2𝑧4 ADP iajs-2703 54 5 + + CCONJ iajs-2703 54 6 ( ( PUNCT iajs-2703 54 7 βˆ’ βˆ’ PROPN iajs-2703 54 8 5 5 NUM iajs-2703 54 9 16 16 NUM iajs-2703 54 10 𝑑3 𝑑3 NOUN iajs-2703 54 11 βˆ’ βˆ’ PROPN iajs-2703 54 12 5 5 NUM iajs-2703 54 13 96 96 NUM iajs-2703 54 14 𝑑4 𝑑4 ADV iajs-2703 54 15 βˆ’ βˆ’ PROPN iajs-2703 54 16 13 13 NUM iajs-2703 54 17 96 96 NUM iajs-2703 54 18 ) ) PUNCT iajs-2703 54 19 𝑧2 𝑧2 NOUN iajs-2703 55 1 + + CCONJ iajs-2703 55 2 1 1 NUM iajs-2703 55 3 ) ) PUNCT iajs-2703 56 1 + + CCONJ iajs-2703 56 2 tan(𝑧 tan(𝑧 X iajs-2703 56 3 ) ) PUNCT iajs-2703 56 4 ( ( PUNCT iajs-2703 56 5 1 1 NUM iajs-2703 56 6 6 6 NUM iajs-2703 56 7 𝑑2𝑧3 𝑑2𝑧3 PROPN iajs-2703 56 8 + + NUM iajs-2703 56 9 2 2 NUM iajs-2703 56 10 ( ( PUNCT iajs-2703 56 11 βˆ’ βˆ’ PROPN iajs-2703 56 12 5 5 NUM iajs-2703 56 13 16 16 NUM iajs-2703 56 14 𝑑3 𝑑3 NOUN iajs-2703 56 15 βˆ’ βˆ’ PROPN iajs-2703 56 16 5 5 NUM iajs-2703 56 17 96 96 NUM iajs-2703 56 18 𝑑4 𝑑4 ADV iajs-2703 56 19 βˆ’ βˆ’ PROPN iajs-2703 56 20 13 13 NUM iajs-2703 56 21 96 96 NUM iajs-2703 56 22 ) ) PUNCT iajs-2703 56 23 𝑧 𝑧 X iajs-2703 56 24 ) ) PUNCT iajs-2703 56 25 βˆ’ βˆ’ PROPN iajs-2703 56 26 1 1 NUM iajs-2703 56 27 120 120 NUM iajs-2703 56 28 𝑧4 𝑧4 ADJ iajs-2703 56 29 βˆ’ βˆ’ PROPN iajs-2703 56 30 ( ( PUNCT iajs-2703 56 31 βˆ’ βˆ’ PROPN iajs-2703 56 32 1 1 NUM iajs-2703 56 33 16 16 NUM iajs-2703 57 1 βˆ’ βˆ’ NUM iajs-2703 57 2 5 5 NUM iajs-2703 57 3 48 48 NUM iajs-2703 57 4 𝑑3 𝑑3 NOUN iajs-2703 57 5 ) ) PUNCT iajs-2703 57 6 𝑧2 𝑧2 NOUN iajs-2703 57 7 βˆ’ βˆ’ PROPN iajs-2703 57 8 7 7 NUM iajs-2703 57 9 32 32 NUM iajs-2703 57 10 βˆ’ βˆ’ NUM iajs-2703 57 11 25 25 NUM iajs-2703 57 12 48 48 NUM iajs-2703 57 13 𝑑3 𝑑3 NOUN iajs-2703 57 14 βˆ’ βˆ’ PROPN iajs-2703 57 15 25 25 NUM iajs-2703 57 16 96 96 NUM iajs-2703 57 17 𝑑4 𝑑4 ADP iajs-2703 57 18 βˆ’ βˆ’ PROPN iajs-2703 57 19 𝑧 𝑧 PROPN iajs-2703 57 20 ( ( PUNCT iajs-2703 57 21 1 1 NUM iajs-2703 57 22 30 30 NUM iajs-2703 57 23 𝑧3 𝑧3 ADJ iajs-2703 57 24 + + CCONJ iajs-2703 57 25 2 2 NUM iajs-2703 57 26 ( ( PUNCT iajs-2703 57 27 βˆ’ βˆ’ PROPN iajs-2703 57 28 1 1 NUM iajs-2703 57 29 16 16 NUM iajs-2703 57 30 βˆ’ βˆ’ NUM iajs-2703 57 31 5 5 NUM iajs-2703 57 32 48 48 NUM iajs-2703 57 33 𝑑3 𝑑3 NOUN iajs-2703 57 34 ) ) PUNCT iajs-2703 57 35 𝑧 𝑧 NOUN iajs-2703 57 36 ) ) PUNCT iajs-2703 57 37 , , PUNCT iajs-2703 57 38 ( ( PUNCT iajs-2703 57 39 7 7 X iajs-2703 57 40 ) ) PUNCT iajs-2703 57 41 𝐷(𝑧 𝐷(𝑧 VERB iajs-2703 57 42 ) ) PUNCT iajs-2703 57 43 = = SYM iajs-2703 57 44 1 1 NUM iajs-2703 57 45 14400 14400 NUM iajs-2703 57 46 𝑧10 𝑧10 NOUN iajs-2703 57 47 + + CCONJ iajs-2703 57 48 ( ( PUNCT iajs-2703 57 49 βˆ’ βˆ’ PROPN iajs-2703 57 50 1 1 NUM iajs-2703 57 51 960 960 NUM iajs-2703 57 52 + + CCONJ iajs-2703 57 53 1 1 NUM iajs-2703 57 54 576 576 NUM iajs-2703 57 55 𝑑2 𝑑2 NOUN iajs-2703 57 56 2 2 NUM iajs-2703 57 57 βˆ’ βˆ’ NUM iajs-2703 57 58 1 1 NUM iajs-2703 57 59 576 576 NUM iajs-2703 57 60 𝑑3 𝑑3 NOUN iajs-2703 57 61 ) ) PUNCT iajs-2703 57 62 𝑧8 𝑧8 PROPN iajs-2703 57 63 + + CCONJ iajs-2703 57 64 ( ( PUNCT iajs-2703 57 65 5 5 NUM iajs-2703 57 66 1152 1152 NUM iajs-2703 57 67 𝑑4 𝑑4 ADV iajs-2703 57 68 + + CCONJ iajs-2703 57 69 29 29 NUM iajs-2703 57 70 3840 3840 NUM iajs-2703 57 71 + + CCONJ iajs-2703 57 72 25 25 NUM iajs-2703 57 73 1152 1152 NUM iajs-2703 57 74 𝑑3 𝑑3 NOUN iajs-2703 57 75 + + CCONJ iajs-2703 57 76 25 25 NUM iajs-2703 57 77 2304 2304 NUM iajs-2703 57 78 𝑑3 𝑑3 NOUN iajs-2703 57 79 2 2 NUM iajs-2703 57 80 βˆ’ βˆ’ PROPN iajs-2703 57 81 5 5 NUM iajs-2703 57 82 1152 1152 NUM iajs-2703 57 83 𝑑2𝑑4 𝑑2𝑑4 X iajs-2703 57 84 βˆ’ βˆ’ PROPN iajs-2703 57 85 13 13 NUM iajs-2703 57 86 1152 1152 NUM iajs-2703 57 87 𝑑2 𝑑2 NOUN iajs-2703 57 88 βˆ’ βˆ’ PROPN iajs-2703 57 89 5 5 NUM iajs-2703 57 90 192 192 NUM iajs-2703 57 91 𝑑2𝑑3 𝑑2𝑑3 NOUN iajs-2703 57 92 ) ) PUNCT iajs-2703 57 93 𝑧6 𝑧6 NOUN iajs-2703 57 94 + + CCONJ iajs-2703 57 95 ( ( PUNCT iajs-2703 57 96 βˆ’ βˆ’ PROPN iajs-2703 57 97 25 25 NUM iajs-2703 57 98 1152 1152 NUM iajs-2703 57 99 𝑑3𝑑4 𝑑3𝑑4 PROPN iajs-2703 58 1 + + CCONJ iajs-2703 58 2 25 25 NUM iajs-2703 58 3 9216 9216 NUM iajs-2703 58 4 𝑑4 𝑑4 ADJ iajs-2703 58 5 2 2 NUM iajs-2703 58 6 + + SYM iajs-2703 58 7 1 1 NUM iajs-2703 58 8 12 12 NUM iajs-2703 58 9 𝑑2 𝑑2 NOUN iajs-2703 58 10 βˆ’ βˆ’ ADP iajs-2703 58 11 25 25 NUM iajs-2703 58 12 2304 2304 NUM iajs-2703 58 13 𝑑3 𝑑3 NOUN iajs-2703 58 14 2 2 NUM iajs-2703 58 15 βˆ’ βˆ’ NOUN iajs-2703 58 16 83 83 NUM iajs-2703 58 17 9216 9216 NUM iajs-2703 58 18 βˆ’ βˆ’ PROPN iajs-2703 58 19 85 85 NUM iajs-2703 58 20 4608 4608 NUM iajs-2703 58 21 𝑑4 𝑑4 VERB iajs-2703 58 22 βˆ’ βˆ’ PROPN iajs-2703 58 23 5 5 NUM iajs-2703 58 24 192 192 NUM iajs-2703 58 25 𝑑3 𝑑3 NOUN iajs-2703 58 26 ) ) PUNCT iajs-2703 58 27 𝑧4 𝑧4 PROPN iajs-2703 58 28 + + CCONJ iajs-2703 58 29 ( ( PUNCT iajs-2703 58 30 βˆ’ βˆ’ PROPN iajs-2703 58 31 685 685 NUM iajs-2703 58 32 3072 3072 NUM iajs-2703 58 33 βˆ’ βˆ’ ADP iajs-2703 58 34 305 305 NUM iajs-2703 58 35 768 768 NUM iajs-2703 58 36 𝑑3 𝑑3 NOUN iajs-2703 58 37 + + CCONJ iajs-2703 58 38 625 625 NUM iajs-2703 58 39 9216 9216 NUM iajs-2703 58 40 𝑑4 𝑑4 ADJ iajs-2703 58 41 2 2 NUM iajs-2703 58 42 + + CCONJ iajs-2703 58 43 625 625 NUM iajs-2703 58 44 2304 2304 NUM iajs-2703 58 45 𝑑3𝑑4 𝑑3𝑑4 PROPN iajs-2703 59 1 + + CCONJ iajs-2703 59 2 625 625 NUM iajs-2703 59 3 2304 2304 NUM iajs-2703 59 4 𝑑3 𝑑3 NOUN iajs-2703 59 5 2 2 NUM iajs-2703 59 6 + + CCONJ iajs-2703 59 7 5 5 NUM iajs-2703 59 8 512 512 NUM iajs-2703 59 9 𝑑4 𝑑4 ADJ iajs-2703 59 10 ) ) PUNCT iajs-2703 59 11 𝑧2 𝑧2 NOUN iajs-2703 59 12 . . PUNCT iajs-2703 60 1 ( ( PUNCT iajs-2703 60 2 8) 8) NUM iajs-2703 60 3 now now ADV iajs-2703 60 4 , , PUNCT iajs-2703 60 5 solving solve VERB iajs-2703 60 6 equations equation NOUN iajs-2703 60 7 ( ( PUNCT iajs-2703 60 8 6),(7 6),(7 NOUN iajs-2703 60 9 ) ) PUNCT iajs-2703 60 10 , , PUNCT iajs-2703 60 11 and and CCONJ iajs-2703 60 12 ( ( PUNCT iajs-2703 60 13 8) 8) NUM iajs-2703 60 14 , , PUNCT iajs-2703 60 15 we we PRON iajs-2703 60 16 get get VERB iajs-2703 60 17 the the DET iajs-2703 60 18 values value NOUN iajs-2703 60 19 of of ADP iajs-2703 60 20 free free ADJ iajs-2703 60 21 parameters parameter NOUN iajs-2703 60 22 in in ADP iajs-2703 60 23 terms term NOUN iajs-2703 60 24 of of ADP iajs-2703 60 25 𝑧 𝑧 NOUN iajs-2703 60 26 , , PUNCT iajs-2703 60 27 and and CCONJ iajs-2703 60 28 the the DET iajs-2703 60 29 expressions expression NOUN iajs-2703 60 30 are be AUX iajs-2703 60 31 too too ADV iajs-2703 60 32 complicated complicated ADJ iajs-2703 60 33 , , PUNCT iajs-2703 60 34 we we PRON iajs-2703 60 35 use use VERB iajs-2703 60 36 the the DET iajs-2703 60 37 following follow VERB iajs-2703 60 38 taylor taylor PROPN iajs-2703 60 39 series series NOUN iajs-2703 60 40 expressions expression NOUN iajs-2703 60 41 , , PUNCT iajs-2703 60 42 𝑑2 𝑑2 NOUN iajs-2703 60 43 = = SYM iajs-2703 60 44 1 1 NUM iajs-2703 60 45 βˆ’ βˆ’ NUM iajs-2703 60 46 29 29 NUM iajs-2703 60 47 630 630 NUM iajs-2703 60 48 𝑧2 𝑧2 NOUN iajs-2703 60 49 βˆ’ βˆ’ PROPN iajs-2703 60 50 311 311 NUM iajs-2703 60 51 75600 75600 NUM iajs-2703 60 52 𝑧4 𝑧4 NOUN iajs-2703 60 53 βˆ’ βˆ’ PROPN iajs-2703 60 54 46369 46369 NUM iajs-2703 60 55 74844000 74844000 NUM iajs-2703 60 56 𝑧6 𝑧6 NOUN iajs-2703 60 57 βˆ’ βˆ’ PROPN iajs-2703 60 58 120976607 120976607 NUM iajs-2703 60 59 1225944720000 1225944720000 NUM iajs-2703 60 60 𝑧8 𝑧8 PROPN iajs-2703 60 61 βˆ’ βˆ’ PROPN iajs-2703 60 62 0 0 NUM iajs-2703 60 63 1 1 NUM iajs-2703 60 64 5 5 NUM iajs-2703 60 65 𝑑2 𝑑2 NOUN iajs-2703 60 66 1 1 NUM iajs-2703 60 67 5 5 NUM iajs-2703 60 68 2 2 NUM iajs-2703 60 69 5 5 NUM iajs-2703 60 70 𝑑3 𝑑3 NOUN iajs-2703 60 71 0 0 NUM iajs-2703 60 72 2 2 NUM iajs-2703 60 73 5 5 NUM iajs-2703 60 74 4 4 NUM iajs-2703 60 75 5 5 NUM iajs-2703 60 76 𝑑4 𝑑4 ADV iajs-2703 60 77 6 6 NUM iajs-2703 60 78 5 5 NUM iajs-2703 60 79 βˆ’ βˆ’ NOUN iajs-2703 60 80 12 12 NUM iajs-2703 60 81 5 5 NUM iajs-2703 60 82 2 2 NUM iajs-2703 60 83 1 1 NUM iajs-2703 60 84 1 1 NUM iajs-2703 60 85 βˆ’ βˆ’ NUM iajs-2703 60 86 17 17 NUM iajs-2703 60 87 8 8 NUM iajs-2703 60 88 5 5 NUM iajs-2703 60 89 βˆ’ βˆ’ NUM iajs-2703 60 90 5 5 NUM iajs-2703 60 91 2 2 NUM iajs-2703 60 92 5 5 NUM iajs-2703 60 93 8 8 NUM iajs-2703 60 94 13 13 NUM iajs-2703 60 95 96 96 NUM iajs-2703 60 96 0 0 NUM iajs-2703 60 97 25 25 NUM iajs-2703 60 98 48 48 NUM iajs-2703 60 99 25 25 NUM iajs-2703 60 100 96 96 NUM iajs-2703 60 101 1 1 NUM iajs-2703 60 102 12 12 NUM iajs-2703 60 103 ibn ibn PROPN iajs-2703 60 104 al al PROPN iajs-2703 60 105 - - PUNCT iajs-2703 60 106 haitham haitham PROPN iajs-2703 60 107 jour jour X iajs-2703 60 108 . . PROPN iajs-2703 61 1 for for ADP iajs-2703 61 2 pure pure ADJ iajs-2703 61 3 & & CCONJ iajs-2703 61 4 appl appl PROPN iajs-2703 61 5 . . PUNCT iajs-2703 62 1 sci sci PROPN iajs-2703 62 2 . . PROPN iajs-2703 63 1 34(4)2021 34(4)2021 NUM iajs-2703 63 2 61 61 NUM iajs-2703 63 3 1756548533 1756548533 NUM iajs-2703 63 4 110335024800000 110335024800000 NUM iajs-2703 63 5 𝑧10 𝑧10 NOUN iajs-2703 63 6 βˆ’ βˆ’ PROPN iajs-2703 63 7 3475880890247 3475880890247 NUM iajs-2703 63 8 1350500703552000000 1350500703552000000 NUM iajs-2703 63 9 𝑧12 𝑧12 NOUN iajs-2703 63 10 βˆ’ βˆ’ PROPN iajs-2703 63 11 β‹― β‹― NOUN iajs-2703 63 12 , , PUNCT iajs-2703 63 13 𝑑3 𝑑3 NOUN iajs-2703 63 14 = = SYM iajs-2703 63 15 1 1 NUM iajs-2703 63 16 βˆ’ βˆ’ NOUN iajs-2703 63 17 4 4 NUM iajs-2703 63 18 1575 1575 NUM iajs-2703 63 19 𝑧4 𝑧4 NOUN iajs-2703 63 20 βˆ’ βˆ’ PROPN iajs-2703 63 21 47 47 NUM iajs-2703 63 22 94500 94500 NUM iajs-2703 63 23 𝑧6 𝑧6 NOUN iajs-2703 63 24 βˆ’ βˆ’ PROPN iajs-2703 63 25 1009 1009 NUM iajs-2703 63 26 13365000 13365000 NUM iajs-2703 63 27 𝑧8 𝑧8 PROPN iajs-2703 63 28 1695769 1695769 NUM iajs-2703 63 29 139311900000 139311900000 NUM iajs-2703 63 30 𝑧10 𝑧10 NOUN iajs-2703 63 31 βˆ’ βˆ’ PROPN iajs-2703 63 32 271269671 271269671 NUM iajs-2703 63 33 137918781000000 137918781000000 NUM iajs-2703 63 34 𝑧12 𝑧12 NOUN iajs-2703 63 35 βˆ’ βˆ’ PROPN iajs-2703 63 36 β‹― β‹― NOUN iajs-2703 63 37 , , PUNCT iajs-2703 63 38 𝑑4 𝑑4 ADV iajs-2703 63 39 = = SYM iajs-2703 63 40 1 1 NUM iajs-2703 63 41 βˆ’ βˆ’ NUM iajs-2703 63 42 8 8 NUM iajs-2703 63 43 1575 1575 NUM iajs-2703 63 44 𝑧4 𝑧4 NOUN iajs-2703 63 45 βˆ’ βˆ’ PROPN iajs-2703 63 46 37 37 NUM iajs-2703 63 47 47250 47250 NUM iajs-2703 63 48 𝑧6 𝑧6 NOUN iajs-2703 63 49 βˆ’ βˆ’ PROPN iajs-2703 63 50 437 437 NUM iajs-2703 63 51 11694375 11694375 NUM iajs-2703 63 52 𝑧8 𝑧8 PROPN iajs-2703 63 53 4558639 4558639 NUM iajs-2703 63 54 766215450000 766215450000 NUM iajs-2703 63 55 𝑧10 𝑧10 NOUN iajs-2703 64 1 βˆ’ βˆ’ PROPN iajs-2703 64 2 32225033 32225033 NUM iajs-2703 64 3 34479695250000 34479695250000 NUM iajs-2703 64 4 𝑧12 𝑧12 NOUN iajs-2703 64 5 βˆ’ βˆ’ PROPN iajs-2703 64 6 β‹―. β‹―. PROPN iajs-2703 64 7 ( ( PUNCT iajs-2703 64 8 9 9 X iajs-2703 64 9 ) ) PUNCT iajs-2703 64 10 it it PRON iajs-2703 64 11 can can AUX iajs-2703 64 12 observe observe VERB iajs-2703 64 13 that that SCONJ iajs-2703 64 14 for for ADP iajs-2703 64 15 𝑧 𝑧 PROPN iajs-2703 64 16 β†’ β†’ SYM iajs-2703 64 17 0 0 NUM iajs-2703 64 18 , , PUNCT iajs-2703 64 19 the the DET iajs-2703 64 20 new new ADJ iajs-2703 64 21 method method NOUN iajs-2703 64 22 reduces reduce VERB iajs-2703 64 23 to to ADP iajs-2703 64 24 an an DET iajs-2703 64 25 original original ADJ iajs-2703 64 26 rk rk NOUN iajs-2703 64 27 method method NOUN iajs-2703 64 28 given give VERB iajs-2703 64 29 in in ADP iajs-2703 64 30 dormand dormand NOUN iajs-2703 64 31 [ [ X iajs-2703 64 32 10 10 NUM iajs-2703 64 33 ] ] PUNCT iajs-2703 64 34 . . 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X iajs-2703 67 4 five five NUM iajs-2703 67 5 - - PUNCT iajs-2703 67 6 stage stage NOUN iajs-2703 67 7 modified modify VERB iajs-2703 67 8 explicit explicit ADJ iajs-2703 67 9 runge runge NOUN iajs-2703 67 10 - - PUNCT iajs-2703 67 11 kutta kutta NOUN iajs-2703 67 12 method method NOUN iajs-2703 67 13 according accord VERB iajs-2703 67 14 to to ADP iajs-2703 67 15 the the DET iajs-2703 67 16 method method NOUN iajs-2703 67 17 in in ADP iajs-2703 67 18 table table NOUN iajs-2703 67 19 3 3 NUM iajs-2703 67 20 , , PUNCT iajs-2703 67 21 the the DET iajs-2703 67 22 phase phase NOUN iajs-2703 67 23 lag lag NOUN iajs-2703 67 24 , , PUNCT iajs-2703 67 25 phase phase NOUN iajs-2703 67 26 lag lag NOUN iajs-2703 67 27 derivative derivative ADJ iajs-2703 67 28 , , PUNCT iajs-2703 67 29 and and CCONJ iajs-2703 67 30 amplification amplification NOUN iajs-2703 67 31 factor factor NOUN iajs-2703 67 32 become become VERB iajs-2703 67 33 𝑃(𝑧 𝑃(𝑧 PRON iajs-2703 67 34 ) ) PUNCT iajs-2703 67 35 = = SYM iajs-2703 67 36 tan(𝑧 tan(𝑧 PROPN iajs-2703 67 37 ) ) PUNCT iajs-2703 67 38 ( ( PUNCT iajs-2703 68 1 1 1 NUM iajs-2703 68 2 + + CCONJ iajs-2703 68 3 ( ( PUNCT iajs-2703 68 4 βˆ’ βˆ’ PROPN iajs-2703 68 5 31 31 NUM iajs-2703 68 6 90 90 NUM iajs-2703 68 7 βˆ’ βˆ’ NUM iajs-2703 68 8 1 1 NUM iajs-2703 68 9 15 15 NUM iajs-2703 68 10 𝑑4 𝑑4 ADP iajs-2703 68 11 βˆ’ βˆ’ PROPN iajs-2703 68 12 4 4 NUM iajs-2703 68 13 45 45 NUM iajs-2703 68 14 𝑑5 𝑑5 PROPN iajs-2703 68 15 ) ) PUNCT iajs-2703 68 16 𝑧2 𝑧2 NOUN iajs-2703 69 1 + + CCONJ iajs-2703 69 2 1 1 NUM iajs-2703 69 3 24 24 NUM iajs-2703 69 4 𝑧4 𝑧4 NOUN iajs-2703 69 5 βˆ’ βˆ’ NUM iajs-2703 69 6 1 1 NUM iajs-2703 69 7 1280 1280 NUM iajs-2703 69 8 𝑧6 𝑧6 NOUN iajs-2703 69 9 ) ) PUNCT iajs-2703 70 1 βˆ’ βˆ’ PROPN iajs-2703 70 2 𝑧 𝑧 PROPN iajs-2703 70 3 ( ( PUNCT iajs-2703 70 4 7 7 NUM iajs-2703 70 5 90 90 NUM iajs-2703 70 6 𝑑6 𝑑6 NOUN iajs-2703 70 7 + + CCONJ iajs-2703 70 8 + + CCONJ iajs-2703 70 9 13 13 NUM iajs-2703 70 10 30 30 NUM iajs-2703 70 11 + + CCONJ iajs-2703 70 12 2 2 NUM iajs-2703 70 13 15 15 NUM iajs-2703 70 14 𝑑4 𝑑4 ADJ iajs-2703 70 15 + + NUM iajs-2703 70 16 16 16 NUM iajs-2703 70 17 45 45 NUM iajs-2703 70 18 𝑑5 𝑑5 PROPN iajs-2703 70 19 + + X iajs-2703 70 20 ( ( PUNCT iajs-2703 70 21 βˆ’ βˆ’ PROPN iajs-2703 70 22 7 7 NUM iajs-2703 70 23 90 90 NUM iajs-2703 70 24 βˆ’ βˆ’ NUM iajs-2703 70 25 1 1 NUM iajs-2703 70 26 20 20 NUM iajs-2703 70 27 𝑑4 𝑑4 ADJ iajs-2703 70 28 ) ) PUNCT iajs-2703 70 29 𝑧2 𝑧2 NOUN iajs-2703 70 30 + + CCONJ iajs-2703 70 31 1 1 NUM iajs-2703 70 32 120 120 NUM iajs-2703 70 33 𝑧4 𝑧4 NUM iajs-2703 70 34 ) ) PUNCT iajs-2703 70 35 ( ( PUNCT iajs-2703 70 36 10 10 NUM iajs-2703 70 37 ) ) PUNCT iajs-2703 70 38 𝑃′(𝑧 𝑃′(𝑧 PROPN iajs-2703 70 39 ) ) PUNCT iajs-2703 70 40 = = PUNCT iajs-2703 70 41 ( ( PUNCT iajs-2703 70 42 1 1 NUM iajs-2703 70 43 + + NUM iajs-2703 70 44 π‘‘π‘Žπ‘›2(𝑧 π‘‘π‘Žπ‘›2(𝑧 NOUN iajs-2703 70 45 ) ) PUNCT iajs-2703 70 46 ) ) PUNCT iajs-2703 70 47 ( ( PUNCT iajs-2703 71 1 1 1 NUM 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74 9 ) ) PUNCT iajs-2703 74 10 𝑧2 𝑧2 NOUN iajs-2703 74 11 βˆ’ βˆ’ PROPN iajs-2703 74 12 1 1 NUM iajs-2703 74 13 120 120 NUM iajs-2703 74 14 𝑧4 𝑧4 NOUN iajs-2703 74 15 βˆ’ βˆ’ X iajs-2703 74 16 𝑧 𝑧 PROPN iajs-2703 74 17 ( ( PUNCT iajs-2703 74 18 1 1 NUM iajs-2703 74 19 30 30 NUM iajs-2703 74 20 𝑧3 𝑧3 ADJ iajs-2703 74 21 + + CCONJ iajs-2703 74 22 2 2 NUM iajs-2703 74 23 ( ( PUNCT iajs-2703 74 24 βˆ’ βˆ’ PROPN iajs-2703 74 25 7 7 NUM iajs-2703 74 26 60 60 NUM iajs-2703 74 27 βˆ’ βˆ’ NUM iajs-2703 74 28 1 1 NUM iajs-2703 74 29 20 20 NUM iajs-2703 74 30 𝑑4 𝑑4 ADJ iajs-2703 74 31 ) ) PUNCT iajs-2703 74 32 𝑧 𝑧 X iajs-2703 74 33 ) ) PUNCT iajs-2703 74 34 , , PUNCT iajs-2703 74 35 ( ( PUNCT iajs-2703 74 36 11 11 NUM iajs-2703 74 37 ) ) PUNCT iajs-2703 74 38 0 0 NUM iajs-2703 74 39 1 1 NUM iajs-2703 74 40 4 4 NUM iajs-2703 74 41 1 1 NUM iajs-2703 74 42 1 1 NUM iajs-2703 74 43 4 4 NUM iajs-2703 74 44 1 1 NUM iajs-2703 74 45 4 4 NUM iajs-2703 74 46 1 1 NUM iajs-2703 74 47 1 1 NUM iajs-2703 74 48 8 8 NUM iajs-2703 74 49 1 1 NUM iajs-2703 74 50 8 8 NUM iajs-2703 74 51 1 1 NUM iajs-2703 74 52 2 2 NUM iajs-2703 74 53 𝑑4 𝑑4 ADV iajs-2703 74 54 0 0 NUM iajs-2703 74 55 0 0 NUM iajs-2703 74 56 1 1 NUM iajs-2703 74 57 2 2 NUM iajs-2703 74 58 3 3 NUM iajs-2703 74 59 4 4 NUM iajs-2703 74 60 𝑑5 𝑑5 PROPN iajs-2703 74 61 3 3 NUM iajs-2703 74 62 16 16 NUM iajs-2703 74 63 βˆ’ βˆ’ NUM iajs-2703 74 64 3 3 NUM iajs-2703 74 65 8 8 NUM iajs-2703 74 66 3 3 NUM iajs-2703 74 67 8 8 NUM iajs-2703 74 68 9 9 NUM iajs-2703 74 69 16 16 NUM iajs-2703 74 70 1 1 NUM iajs-2703 74 71 𝑑6 𝑑6 NOUN iajs-2703 74 72 βˆ’ βˆ’ PROPN iajs-2703 74 73 3 3 NUM iajs-2703 74 74 7 7 NUM iajs-2703 74 75 8 8 NUM iajs-2703 74 76 7 7 NUM iajs-2703 74 77 6 6 NUM iajs-2703 74 78 7 7 NUM iajs-2703 74 79 βˆ’ βˆ’ NOUN iajs-2703 74 80 12 12 NUM iajs-2703 74 81 7 7 NUM iajs-2703 74 82 8 8 NUM iajs-2703 74 83 7 7 NUM iajs-2703 74 84 7 7 NUM iajs-2703 74 85 90 90 NUM iajs-2703 74 86 0 0 NUM iajs-2703 74 87 16 16 NUM iajs-2703 74 88 45 45 NUM iajs-2703 74 89 2 2 NUM iajs-2703 74 90 15 15 NUM iajs-2703 74 91 16 16 NUM iajs-2703 74 92 45 45 NUM iajs-2703 74 93 7 7 NUM iajs-2703 74 94 90 90 NUM iajs-2703 74 95 ibn ibn PROPN iajs-2703 74 96 al al PROPN iajs-2703 74 97 - - PUNCT iajs-2703 74 98 haitham haitham PROPN iajs-2703 74 99 jour jour X iajs-2703 74 100 . . PROPN iajs-2703 75 1 for for ADP iajs-2703 75 2 pure pure ADJ iajs-2703 75 3 & & CCONJ iajs-2703 75 4 appl appl PROPN iajs-2703 75 5 . . PUNCT iajs-2703 76 1 sci sci PROPN iajs-2703 76 2 . . PROPN iajs-2703 77 1 34(4)2021 34(4)2021 NUM iajs-2703 77 2 62 62 NUM iajs-2703 77 3 𝐷(𝑧 𝐷(𝑧 NOUN iajs-2703 77 4 ) ) PUNCT iajs-2703 77 5 = = SYM iajs-2703 77 6 1 1 NUM iajs-2703 77 7 1638400 1638400 NUM iajs-2703 77 8 𝑧12 𝑧12 NOUN iajs-2703 77 9 + + CCONJ iajs-2703 77 10 1 1 NUM iajs-2703 77 11 230400 230400 NUM iajs-2703 77 12 𝑧10 𝑧10 NOUN iajs-2703 78 1 + + CCONJ iajs-2703 78 2 ( ( PUNCT iajs-2703 78 3 19 19 NUM iajs-2703 78 4 57600 57600 NUM iajs-2703 78 5 βˆ’ βˆ’ NOUN iajs-2703 78 6 7 7 NUM iajs-2703 78 7 9600 9600 NUM iajs-2703 78 8 𝑑4 𝑑4 ADJ iajs-2703 78 9 + + CCONJ iajs-2703 78 10 1 1 NUM iajs-2703 78 11 7200 7200 NUM iajs-2703 78 12 𝑑5 𝑑5 PROPN iajs-2703 78 13 ) ) PUNCT iajs-2703 78 14 𝑧8 𝑧8 PROPN iajs-2703 78 15 + + CCONJ iajs-2703 78 16 ( ( PUNCT iajs-2703 78 17 1 1 NUM iajs-2703 78 18 120 120 NUM iajs-2703 78 19 𝑑4 𝑑4 ADV iajs-2703 78 20 βˆ’ βˆ’ PROPN iajs-2703 78 21 1 1 NUM iajs-2703 78 22 675 675 NUM iajs-2703 78 23 𝑑5 𝑑5 PROPN iajs-2703 78 24 + + CCONJ iajs-2703 78 25 1 1 NUM iajs-2703 78 26 400 400 NUM iajs-2703 78 27 𝑑4 𝑑4 ADV iajs-2703 78 28 2 2 NUM iajs-2703 78 29 βˆ’ βˆ’ PROPN iajs-2703 78 30 163 163 NUM iajs-2703 78 31 17280 17280 NUM iajs-2703 78 32 + + CCONJ iajs-2703 78 33 7 7 NUM iajs-2703 78 34 5400 5400 NUM iajs-2703 78 35 𝑑6 𝑑6 NOUN iajs-2703 78 36 ) ) PUNCT iajs-2703 78 37 𝑧6 𝑧6 PROPN iajs-2703 78 38 + + CCONJ iajs-2703 78 39 ( ( PUNCT iajs-2703 78 40 βˆ’ βˆ’ PROPN iajs-2703 78 41 77 77 NUM iajs-2703 78 42 2700 2700 NUM iajs-2703 78 43 𝑑4 𝑑4 ADV iajs-2703 78 44 βˆ’ βˆ’ PROPN iajs-2703 78 45 2 2 NUM iajs-2703 78 46 225 225 NUM iajs-2703 78 47 𝑑4 𝑑4 ADV iajs-2703 78 48 2 2 NUM iajs-2703 78 49 βˆ’ βˆ’ NOUN iajs-2703 78 50 44 44 NUM iajs-2703 78 51 2025 2025 NUM iajs-2703 78 52 𝑑5 𝑑5 PROPN iajs-2703 78 53 + + CCONJ iajs-2703 78 54 817 817 NUM iajs-2703 78 55 8100 8100 NUM iajs-2703 78 56 βˆ’ βˆ’ NUM iajs-2703 78 57 49 49 NUM iajs-2703 78 58 2700 2700 NUM iajs-2703 79 1 𝑑6 𝑑6 NOUN iajs-2703 79 2 βˆ’ βˆ’ PROPN iajs-2703 79 3 7 7 NUM iajs-2703 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CCONJ iajs-2703 82 1 112 112 NUM iajs-2703 82 2 2025 2025 NUM iajs-2703 82 3 𝑑5𝑑6 𝑑5𝑑6 DET iajs-2703 82 4 + + NUM iajs-2703 82 5 14 14 NUM iajs-2703 82 6 675 675 NUM iajs-2703 82 7 𝑑4𝑑6 𝑑4𝑑6 NOUN iajs-2703 82 8 + + CCONJ iajs-2703 82 9 + + CCONJ iajs-2703 82 10 91 91 NUM iajs-2703 82 11 1350 1350 NUM iajs-2703 82 12 𝑑6 𝑑6 NOUN iajs-2703 82 13 βˆ’ βˆ’ PROPN iajs-2703 82 14 4 4 NUM iajs-2703 82 15 225 225 NUM iajs-2703 82 16 𝑑4 𝑑4 ADV iajs-2703 82 17 βˆ’ βˆ’ PROPN iajs-2703 82 18 451 451 NUM iajs-2703 82 19 900 900 NUM iajs-2703 82 20 ) ) PUNCT iajs-2703 82 21 𝑧2 𝑧2 NOUN iajs-2703 82 22 ( ( PUNCT iajs-2703 82 23 12 12 NUM iajs-2703 82 24 ) ) PUNCT iajs-2703 82 25 solving solve VERB iajs-2703 82 26 equations equation NOUN iajs-2703 82 27 ( ( PUNCT iajs-2703 82 28 10),(11 10),(11 NOUN iajs-2703 82 29 ) ) PUNCT iajs-2703 82 30 , , PUNCT iajs-2703 82 31 and and CCONJ iajs-2703 82 32 ( ( PUNCT iajs-2703 82 33 12 12 NUM iajs-2703 82 34 ) ) PUNCT iajs-2703 82 35 , , PUNCT iajs-2703 82 36 we we PRON iajs-2703 82 37 find find VERB iajs-2703 82 38 𝑑4 𝑑4 ADV iajs-2703 82 39 = = SYM iajs-2703 83 1 1 1 NUM iajs-2703 83 2 βˆ’ βˆ’ NUM iajs-2703 83 3 25 25 NUM iajs-2703 83 4 2016 2016 NUM iajs-2703 83 5 𝑧4 𝑧4 NOUN iajs-2703 83 6 βˆ’ βˆ’ NUM iajs-2703 83 7 31 31 NUM iajs-2703 83 8 4536 4536 NUM iajs-2703 83 9 𝑧6 𝑧6 NOUN iajs-2703 83 10 βˆ’ βˆ’ PROPN iajs-2703 83 11 613 613 NUM iajs-2703 83 12 221760 221760 NUM iajs-2703 83 13 𝑧8 𝑧8 PROPN iajs-2703 83 14 βˆ’ βˆ’ PROPN iajs-2703 83 15 116287 116287 NUM iajs-2703 83 16 103783680 103783680 NUM iajs-2703 83 17 𝑧10 𝑧10 NOUN iajs-2703 83 18 βˆ’ βˆ’ PROPN iajs-2703 83 19 5938297 5938297 NUM iajs-2703 83 20 1307643680 1307643680 NUM iajs-2703 83 21 𝑧12 𝑧12 VERB iajs-2703 83 22 βˆ’ βˆ’ PROPN iajs-2703 83 23 3273113521 3273113521 NUM iajs-2703 83 24 17784371404800 17784371404800 NUM iajs-2703 83 25 𝑧14 𝑧14 NOUN iajs-2703 83 26 βˆ’ βˆ’ PROPN iajs-2703 83 27 β‹― β‹― PROPN iajs-2703 83 28 , , PUNCT iajs-2703 83 29 𝑑5 𝑑5 PROPN iajs-2703 83 30 = = PROPN iajs-2703 83 31 1 1 NUM iajs-2703 83 32 + + NUM iajs-2703 83 33 347 347 NUM iajs-2703 83 34 21504 21504 NUM iajs-2703 83 35 𝑧4 𝑧4 NOUN iajs-2703 83 36 + + CCONJ iajs-2703 83 37 67 67 NUM iajs-2703 83 38 13824 13824 NUM iajs-2703 83 39 𝑧6 𝑧6 NOUN iajs-2703 83 40 + + CCONJ iajs-2703 83 41 7367 7367 NUM iajs-2703 83 42 3548160 3548160 NUM iajs-2703 83 43 𝑧8 𝑧8 PROPN iajs-2703 83 44 + + CCONJ iajs-2703 83 45 2819 2819 NUM iajs-2703 83 46 3354624 3354624 NUM iajs-2703 83 47 𝑧10 𝑧10 NOUN iajs-2703 84 1 + + CCONJ iajs-2703 84 2 1827169 1827169 NUM iajs-2703 84 3 5364817920 5364817920 NUM iajs-2703 84 4 𝑧12 𝑧12 NOUN iajs-2703 84 5 + + CCONJ iajs-2703 84 6 13092454033 13092454033 NUM iajs-2703 84 7 94849980825600 94849980825600 NUM iajs-2703 84 8 𝑧14 𝑧14 NOUN iajs-2703 84 9 + + CCONJ iajs-2703 84 10 β‹― β‹― NOUN iajs-2703 84 11 , , PUNCT iajs-2703 84 12 𝑑6 𝑑6 NOUN iajs-2703 84 13 = = NOUN iajs-2703 84 14 1 1 NUM iajs-2703 84 15 βˆ’ βˆ’ NUM iajs-2703 84 16 247 247 NUM iajs-2703 84 17 4704 4704 NUM iajs-2703 84 18 𝑧4 𝑧4 NOUN iajs-2703 84 19 βˆ’ βˆ’ PROPN iajs-2703 84 20 1775 1775 NUM iajs-2703 84 21 84672 84672 NUM iajs-2703 84 22 𝑧6 𝑧6 PROPN iajs-2703 84 23 βˆ’ βˆ’ PROPN iajs-2703 84 24 14143 14143 NUM iajs-2703 84 25 1552320 1552320 NUM iajs-2703 84 26 𝑧8 𝑧8 PROPN iajs-2703 84 27 βˆ’ βˆ’ PROPN iajs-2703 84 28 447763 447763 NUM iajs-2703 84 29 121080960 121080960 NUM iajs-2703 84 30 𝑧10 𝑧10 NOUN iajs-2703 84 31 βˆ’ βˆ’ PROPN iajs-2703 84 32 22865693 22865693 NUM iajs-2703 84 33 15256200960 15256200960 NUM iajs-2703 84 34 𝑧12 𝑧12 NOUN iajs-2703 84 35 βˆ’ βˆ’ PROPN iajs-2703 84 36 2520658027 2520658027 NUM iajs-2703 84 37 4149686661120 4149686661120 NUM iajs-2703 84 38 𝑧14 𝑧14 NOUN iajs-2703 84 39 βˆ’ βˆ’ PROPN iajs-2703 84 40 β‹―. β‹―. PROPN iajs-2703 84 41 ( ( PUNCT iajs-2703 84 42 13 13 NUM iajs-2703 84 43 ) ) PUNCT iajs-2703 84 44 it it PRON iajs-2703 84 45 can can AUX iajs-2703 84 46 demonstrate demonstrate VERB iajs-2703 84 47 that that SCONJ iajs-2703 84 48 for for ADP iajs-2703 84 49 𝑧 𝑧 PROPN iajs-2703 84 50 β†’ β†’ SYM iajs-2703 84 51 0 0 NUM iajs-2703 84 52 , , PUNCT iajs-2703 84 53 the the DET iajs-2703 84 54 new new ADJ iajs-2703 84 55 method method NOUN iajs-2703 84 56 same same ADJ iajs-2703 84 57 as as ADP iajs-2703 84 58 the the DET iajs-2703 84 59 original original ADJ iajs-2703 84 60 rk rk NOUN iajs-2703 84 61 method method NOUN iajs-2703 84 62 given give VERB iajs-2703 84 63 in in ADP iajs-2703 84 64 butcher butcher NOUN iajs-2703 85 1 [ [ X iajs-2703 85 2 3 3 NUM iajs-2703 85 3 ] ] PUNCT iajs-2703 85 4 . . PUNCT iajs-2703 86 1 4 4 X iajs-2703 86 2 . . X iajs-2703 86 3 numerical numerical ADJ iajs-2703 86 4 results result NOUN iajs-2703 86 5 to to PART iajs-2703 86 6 evaluate evaluate VERB iajs-2703 86 7 the the DET iajs-2703 86 8 performance performance NOUN iajs-2703 86 9 of of ADP iajs-2703 86 10 the the DET iajs-2703 86 11 new new ADJ iajs-2703 86 12 modified modify VERB iajs-2703 86 13 runge runge NOUN iajs-2703 86 14 - - PUNCT iajs-2703 86 15 kutta kutta NOUN iajs-2703 86 16 methods method NOUN iajs-2703 86 17 suggested suggest VERB iajs-2703 86 18 in in ADP iajs-2703 86 19 this this DET iajs-2703 86 20 paper paper NOUN iajs-2703 86 21 , , PUNCT iajs-2703 86 22 we we PRON iajs-2703 86 23 apply apply VERB iajs-2703 86 24 them they PRON iajs-2703 86 25 to to ADP iajs-2703 86 26 five five NUM iajs-2703 86 27 oscillatory oscillatory ADJ iajs-2703 86 28 problems problem NOUN iajs-2703 86 29 and and CCONJ iajs-2703 86 30 then then ADV iajs-2703 86 31 compared compare VERB iajs-2703 86 32 the the DET iajs-2703 86 33 numerical numerical ADJ iajs-2703 86 34 results result NOUN iajs-2703 86 35 with with ADP iajs-2703 86 36 the the DET iajs-2703 86 37 several several ADJ iajs-2703 86 38 well well ADV iajs-2703 86 39 - - PUNCT iajs-2703 86 40 known know VERB iajs-2703 86 41 efficient efficient ADJ iajs-2703 86 42 methods method NOUN iajs-2703 86 43 . . PUNCT iajs-2703 87 1 we we PRON iajs-2703 87 2 use use VERB iajs-2703 87 3 the the DET iajs-2703 87 4 criteria criterion NOUN iajs-2703 87 5 of of ADP iajs-2703 87 6 absolute absolute ADJ iajs-2703 87 7 error error NOUN iajs-2703 87 8 to to PART iajs-2703 87 9 measure measure VERB iajs-2703 87 10 the the DET iajs-2703 87 11 accuracy accuracy NOUN iajs-2703 87 12 of of ADP iajs-2703 87 13 the the DET iajs-2703 87 14 method method NOUN iajs-2703 87 15 , , PUNCT iajs-2703 87 16 which which PRON iajs-2703 87 17 is be AUX iajs-2703 87 18 given give VERB iajs-2703 87 19 by by ADP iajs-2703 87 20 absolute absolute ADJ iajs-2703 87 21 error error NOUN iajs-2703 87 22 = = SYM iajs-2703 87 23 max max PROPN iajs-2703 87 24 ( ( PUNCT iajs-2703 87 25 |𝑦(𝑑𝑛 |𝑦(𝑑𝑛 PROPN iajs-2703 87 26 ) ) PUNCT iajs-2703 87 27 βˆ’ βˆ’ PROPN iajs-2703 88 1 𝑦𝑛| 𝑦𝑛| PROPN iajs-2703 88 2 ) ) PUNCT iajs-2703 88 3 . . PUNCT iajs-2703 89 1 where where SCONJ iajs-2703 89 2 𝑦(𝑑𝑛 𝑦(𝑑𝑛 NOUN iajs-2703 89 3 ) ) PUNCT iajs-2703 89 4 is be AUX iajs-2703 89 5 the the DET iajs-2703 89 6 true true ADJ iajs-2703 89 7 solution solution NOUN iajs-2703 89 8 and and CCONJ iajs-2703 89 9 𝑦𝑛 𝑦𝑛 NOUN iajs-2703 89 10 is be AUX iajs-2703 89 11 the the DET iajs-2703 89 12 numerical numerical ADJ iajs-2703 89 13 solution solution NOUN iajs-2703 89 14 . . PUNCT iajs-2703 90 1 figures figure NOUN iajs-2703 90 2 1 1 NUM iajs-2703 90 3 - - SYM iajs-2703 90 4 5 5 NUM iajs-2703 90 5 demonstrate demonstrate VERB iajs-2703 90 6 the the DET iajs-2703 90 7 efficiency efficiency NOUN iajs-2703 90 8 graphs graph NOUN iajs-2703 90 9 of of ADP iajs-2703 90 10 log log NOUN iajs-2703 90 11 10 10 NUM iajs-2703 90 12 ( ( PUNCT iajs-2703 90 13 max max PROPN iajs-2703 90 14 error error NOUN iajs-2703 90 15 ) ) PUNCT iajs-2703 90 16 versus versus ADP iajs-2703 90 17 step step NOUN iajs-2703 90 18 size size NOUN iajs-2703 90 19 β„Ž. β„Ž. NOUN iajs-2703 90 20 integration integration NOUN iajs-2703 90 21 interval interval NOUN iajs-2703 90 22 is be AUX iajs-2703 90 23 [ [ X iajs-2703 90 24 0 0 NUM iajs-2703 90 25 , , PUNCT iajs-2703 90 26 1000 1000 NUM iajs-2703 90 27 ] ] PUNCT iajs-2703 90 28 for for ADP iajs-2703 90 29 all all DET iajs-2703 90 30 problems problem NOUN iajs-2703 90 31 with with ADP iajs-2703 90 32 step step NOUN iajs-2703 90 33 sizes size NOUN iajs-2703 91 1 β„Ž β„Ž PROPN iajs-2703 91 2 = = SYM iajs-2703 91 3 0.1 0.1 NUM iajs-2703 91 4 2𝑖 2𝑖 NOUN iajs-2703 91 5 , , PUNCT iajs-2703 91 6 𝑖 𝑖 PROPN iajs-2703 91 7 = = SYM iajs-2703 91 8 1,2,3,4 1,2,3,4 NUM iajs-2703 91 9 ⁄ ⁄ NOUN iajs-2703 91 10 . . PUNCT iajs-2703 92 1 the the DET iajs-2703 92 2 following follow VERB iajs-2703 92 3 numerical numerical ADJ iajs-2703 92 4 methods method NOUN iajs-2703 92 5 are be AUX iajs-2703 92 6 used use VERB iajs-2703 92 7 in in ADP iajs-2703 92 8 the the DET iajs-2703 92 9 comparison comparison NOUN iajs-2703 92 10 . . PUNCT iajs-2703 93 1 ( ( PUNCT iajs-2703 93 2 i i NOUN iajs-2703 93 3 ) ) PUNCT iajs-2703 93 4 ο‚· ο‚· NOUN iajs-2703 94 1 mrk4 mrk4 PROPN iajs-2703 94 2 : : PUNCT iajs-2703 94 3 modified modify VERB iajs-2703 94 4 five five NUM iajs-2703 94 5 - - PUNCT iajs-2703 94 6 stage stage NOUN iajs-2703 94 7 fourth fourth ADJ iajs-2703 94 8 - - PUNCT iajs-2703 94 9 order order NOUN iajs-2703 94 10 rk rk NOUN iajs-2703 94 11 method method NOUN iajs-2703 94 12 presented present VERB iajs-2703 94 13 in in ADP iajs-2703 94 14 table table NOUN iajs-2703 94 15 1 1 NUM iajs-2703 94 16 and and CCONJ iajs-2703 94 17 eqs eqs X iajs-2703 94 18 . . PUNCT iajs-2703 95 1 ( ( PUNCT iajs-2703 95 2 9 9 NUM iajs-2703 95 3 ) ) PUNCT iajs-2703 95 4 in in ADP iajs-2703 95 5 section section NOUN iajs-2703 95 6 3 3 NUM iajs-2703 95 7 in in ADP iajs-2703 95 8 this this DET iajs-2703 95 9 paper paper NOUN iajs-2703 95 10 . . PUNCT iajs-2703 96 1 ο‚· ο‚· X iajs-2703 96 2 rk4d rk4d NOUN iajs-2703 96 3 : : PUNCT iajs-2703 96 4 the the DET iajs-2703 96 5 classical classical ADJ iajs-2703 96 6 five five NUM iajs-2703 96 7 - - PUNCT iajs-2703 96 8 stage stage NOUN iajs-2703 96 9 rk rk NOUN iajs-2703 96 10 method method NOUN iajs-2703 96 11 of of ADP iajs-2703 96 12 order order NOUN iajs-2703 96 13 four four NUM iajs-2703 96 14 given give VERB iajs-2703 96 15 in in ADP iajs-2703 96 16 [ [ X iajs-2703 96 17 10 10 NUM iajs-2703 96 18 ] ] PUNCT iajs-2703 96 19 . . PUNCT iajs-2703 97 1 ο‚· ο‚· PROPN iajs-2703 97 2 rk4pf rk4pf NOUN iajs-2703 97 3 : : PUNCT iajs-2703 97 4 the the DET iajs-2703 97 5 phase phase NOUN iajs-2703 97 6 - - PUNCT iajs-2703 97 7 fitted fit VERB iajs-2703 97 8 and and CCONJ iajs-2703 97 9 amplification amplification NOUN iajs-2703 97 10 - - PUNCT iajs-2703 97 11 fitted fit VERB iajs-2703 97 12 rk rk NOUN iajs-2703 97 13 method method NOUN iajs-2703 97 14 given give VERB iajs-2703 97 15 in in ADP iajs-2703 97 16 [ [ X iajs-2703 97 17 7 7 NUM iajs-2703 97 18 ] ] X iajs-2703 97 19 . . PUNCT iajs-2703 98 1 ο‚· ο‚· PUNCT iajs-2703 98 2 rk5s rk5 NOUN iajs-2703 98 3 : : PUNCT iajs-2703 98 4 six six NUM iajs-2703 98 5 - - PUNCT iajs-2703 98 6 stage stage NOUN iajs-2703 98 7 rk rk NOUN iajs-2703 98 8 method method NOUN iajs-2703 98 9 of of ADP iajs-2703 98 10 order order NOUN iajs-2703 98 11 five five NUM iajs-2703 98 12 given give VERB iajs-2703 98 13 in in ADP iajs-2703 98 14 [ [ X iajs-2703 98 15 11 11 NUM iajs-2703 98 16 ] ] PUNCT iajs-2703 98 17 . . PUNCT iajs-2703 99 1 ο‚· ο‚· NOUN iajs-2703 99 2 rk4ms rk4m NOUN iajs-2703 99 3 : : PUNCT iajs-2703 99 4 the the DET iajs-2703 99 5 modified modified ADJ iajs-2703 99 6 four four NUM iajs-2703 99 7 - - PUNCT iajs-2703 99 8 order order NOUN iajs-2703 99 9 rk rk NOUN iajs-2703 99 10 method method NOUN iajs-2703 99 11 given give VERB iajs-2703 99 12 in in ADP iajs-2703 99 13 [ [ NOUN iajs-2703 99 14 9 9 NUM iajs-2703 99 15 ] ] PUNCT iajs-2703 99 16 . . PUNCT iajs-2703 100 1 ibn ibn PROPN iajs-2703 100 2 al al PROPN iajs-2703 100 3 - - PUNCT iajs-2703 100 4 haitham haitham PROPN iajs-2703 100 5 jour jour X iajs-2703 100 6 . . PROPN iajs-2703 100 7 for for ADP iajs-2703 100 8 pure pure ADJ iajs-2703 100 9 & & CCONJ iajs-2703 100 10 appl appl PROPN iajs-2703 100 11 . . PUNCT iajs-2703 101 1 sci sci PROPN iajs-2703 101 2 . . PROPN iajs-2703 102 1 34(4)2021 34(4)2021 NUM iajs-2703 102 2 63 63 NUM iajs-2703 102 3 ο‚· ο‚· NOUN iajs-2703 102 4 rk4b rk4b NOUN iajs-2703 102 5 : : PUNCT iajs-2703 102 6 the the DET iajs-2703 102 7 five five NUM iajs-2703 102 8 - - PUNCT iajs-2703 102 9 stage stage NOUN iajs-2703 102 10 rk rk NOUN iajs-2703 102 11 method method NOUN iajs-2703 102 12 of of ADP iajs-2703 102 13 fourth fourth ADJ iajs-2703 102 14 - - PUNCT iajs-2703 102 15 order order NOUN iajs-2703 102 16 given give VERB iajs-2703 102 17 in in ADP iajs-2703 102 18 [ [ X iajs-2703 102 19 3 3 NUM iajs-2703 102 20 ] ] PUNCT iajs-2703 102 21 . . PUNCT iajs-2703 103 1 ( ( PUNCT iajs-2703 103 2 ii ii NOUN iajs-2703 103 3 ) ) PUNCT iajs-2703 103 4 ο‚· ο‚· NOUN iajs-2703 103 5 mrk5 mrk5 PROPN iajs-2703 103 6 : : PUNCT iajs-2703 103 7 modified modify VERB iajs-2703 103 8 six six NUM iajs-2703 103 9 - - PUNCT iajs-2703 103 10 stage stage NOUN iajs-2703 103 11 fifth fifth ADJ iajs-2703 103 12 - - PUNCT iajs-2703 103 13 order order NOUN iajs-2703 103 14 rk rk NOUN iajs-2703 103 15 method method NOUN iajs-2703 103 16 presented present VERB iajs-2703 103 17 in in ADP iajs-2703 103 18 table table NOUN iajs-2703 103 19 2 2 NUM iajs-2703 103 20 and and CCONJ iajs-2703 103 21 eqs eqs X iajs-2703 103 22 . . PUNCT iajs-2703 104 1 ( ( PUNCT iajs-2703 104 2 13 13 NUM iajs-2703 104 3 ) ) PUNCT iajs-2703 104 4 in in ADP iajs-2703 104 5 section section NOUN iajs-2703 104 6 3 3 NUM iajs-2703 104 7 in in ADP iajs-2703 104 8 this this DET iajs-2703 104 9 paper paper NOUN iajs-2703 104 10 . . PUNCT iajs-2703 105 1 ο‚· ο‚· X iajs-2703 106 1 rk5b rk5b NOUN iajs-2703 106 2 : : PUNCT iajs-2703 106 3 the the DET iajs-2703 106 4 classical classical ADJ iajs-2703 106 5 six six NUM iajs-2703 106 6 - - PUNCT iajs-2703 106 7 stage stage NOUN iajs-2703 106 8 rk rk NOUN iajs-2703 106 9 method method NOUN iajs-2703 106 10 of of ADP iajs-2703 106 11 order order NOUN iajs-2703 106 12 five five NUM iajs-2703 106 13 given give VERB iajs-2703 106 14 in in ADP iajs-2703 106 15 [ [ X iajs-2703 106 16 3 3 NUM iajs-2703 106 17 ] ] PUNCT iajs-2703 106 18 . . PUNCT iajs-2703 107 1 ο‚· ο‚· PROPN iajs-2703 107 2 ork5 ork5 PROPN iajs-2703 107 3 t t PROPN iajs-2703 107 4 : : PUNCT iajs-2703 107 5 optimized optimize VERB iajs-2703 107 6 fifth fifth ADJ iajs-2703 107 7 - - PUNCT iajs-2703 107 8 order order NOUN iajs-2703 107 9 rk rk NOUN iajs-2703 107 10 method method NOUN iajs-2703 107 11 given give VERB iajs-2703 107 12 in in ADP iajs-2703 107 13 [ [ X iajs-2703 107 14 4 4 NUM iajs-2703 107 15 ] ] PUNCT iajs-2703 107 16 . . PUNCT iajs-2703 108 1 ο‚· ο‚· PROPN iajs-2703 109 1 rk5 rk5 PROPN iajs-2703 109 2 m m PROPN iajs-2703 109 3 : : PUNCT iajs-2703 109 4 optimized optimize VERB iajs-2703 109 5 rk rk NOUN iajs-2703 109 6 method method NOUN iajs-2703 109 7 of of ADP iajs-2703 109 8 order order NOUN iajs-2703 109 9 five five NUM iajs-2703 109 10 given give VERB iajs-2703 109 11 in in ADP iajs-2703 109 12 [ [ X iajs-2703 109 13 12 12 NUM iajs-2703 109 14 ] ] PUNCT iajs-2703 109 15 . . PUNCT iajs-2703 110 1 ο‚· ο‚· ADJ iajs-2703 110 2 ork5a ork5a PROPN iajs-2703 110 3 : : PUNCT iajs-2703 110 4 optimized optimize VERB iajs-2703 110 5 rk rk NOUN iajs-2703 110 6 method method NOUN iajs-2703 110 7 of of ADP iajs-2703 110 8 order order NOUN iajs-2703 110 9 five five NUM iajs-2703 110 10 given give VERB iajs-2703 110 11 in in ADP iajs-2703 110 12 [ [ X iajs-2703 110 13 5 5 NUM iajs-2703 110 14 ] ] PUNCT iajs-2703 110 15 . . PUNCT iajs-2703 111 1 ο‚· ο‚· X iajs-2703 111 2 rk5k rk5k ADJ iajs-2703 111 3 : : PUNCT iajs-2703 111 4 optimized optimize VERB iajs-2703 111 5 fifth fifth ADJ iajs-2703 111 6 - - PUNCT iajs-2703 111 7 order order NOUN iajs-2703 111 8 rk rk NOUN iajs-2703 111 9 method method NOUN iajs-2703 111 10 proposed propose VERB iajs-2703 111 11 in in ADP iajs-2703 111 12 [ [ X iajs-2703 111 13 6 6 NUM iajs-2703 111 14 ] ] PUNCT iajs-2703 111 15 . . PUNCT iajs-2703 112 1 problem problem NOUN iajs-2703 112 2 1 1 NUM iajs-2703 112 3 : : PUNCT iajs-2703 113 1 [ [ X iajs-2703 113 2 13 13 NUM iajs-2703 113 3 ] ] PUNCT iajs-2703 113 4 𝑒′′(𝑑 𝑒′′(𝑑 NOUN iajs-2703 113 5 ) ) PUNCT iajs-2703 113 6 = = PUNCT iajs-2703 113 7 100 100 NUM iajs-2703 113 8 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 113 9 ) ) PUNCT iajs-2703 113 10 + + CCONJ iajs-2703 113 11 99 99 NUM iajs-2703 113 12 sin(𝑑 sin(𝑑 NOUN iajs-2703 113 13 ) ) PUNCT iajs-2703 113 14 , , PUNCT iajs-2703 113 15 𝑒(0 𝑒(0 PROPN iajs-2703 113 16 ) ) PUNCT iajs-2703 113 17 = = SYM iajs-2703 113 18 1 1 NUM iajs-2703 113 19 , , PUNCT iajs-2703 113 20 𝑒′(0 𝑒′(0 NOUN iajs-2703 113 21 ) ) PUNCT iajs-2703 113 22 = = SYM iajs-2703 113 23 11 11 NUM iajs-2703 113 24 . . PUNCT iajs-2703 114 1 whose whose DET iajs-2703 114 2 exact exact ADJ iajs-2703 114 3 solution solution NOUN iajs-2703 114 4 is be AUX iajs-2703 114 5 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 114 6 ) ) PUNCT iajs-2703 114 7 = = SYM iajs-2703 114 8 cos(10𝑑 cos(10𝑑 X iajs-2703 114 9 ) ) PUNCT iajs-2703 115 1 + + CCONJ iajs-2703 115 2 sin(10𝑑 sin(10𝑑 X iajs-2703 115 3 ) ) PUNCT iajs-2703 115 4 + + CCONJ iajs-2703 115 5 sin(𝑑 sin(𝑑 PROPN iajs-2703 115 6 ) ) PUNCT iajs-2703 115 7 , , PUNCT iajs-2703 115 8 and and CCONJ iajs-2703 115 9 𝑀 𝑀 X iajs-2703 115 10 = = SYM iajs-2703 115 11 10 10 NUM iajs-2703 115 12 . . PUNCT iajs-2703 116 1 problem problem NOUN iajs-2703 116 2 2 2 NUM iajs-2703 116 3 : : PUNCT iajs-2703 117 1 [ [ X iajs-2703 117 2 14 14 NUM iajs-2703 117 3 ] ] PUNCT iajs-2703 117 4 𝑒′′(𝑑 𝑒′′(𝑑 NOUN iajs-2703 117 5 ) ) PUNCT iajs-2703 117 6 = = SYM iajs-2703 117 7 βˆ’64 βˆ’64 NOUN iajs-2703 117 8 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 117 9 ) ) PUNCT iajs-2703 117 10 , , PUNCT iajs-2703 117 11 𝑒(0 𝑒(0 PROPN iajs-2703 117 12 ) ) PUNCT iajs-2703 117 13 = = SYM iajs-2703 117 14 1 1 NUM iajs-2703 117 15 , , PUNCT iajs-2703 117 16 𝑒′(0 𝑒′(0 NOUN iajs-2703 117 17 ) ) PUNCT iajs-2703 117 18 = = SYM iajs-2703 117 19 βˆ’2 βˆ’2 NOUN iajs-2703 117 20 . . PUNCT iajs-2703 118 1 exact exact ADJ iajs-2703 118 2 solution solution NOUN iajs-2703 118 3 is be AUX iajs-2703 118 4 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 118 5 ) ) PUNCT iajs-2703 118 6 = = SYM iajs-2703 118 7 1 1 NUM iajs-2703 118 8 4 4 NUM iajs-2703 118 9 sin(8𝑑 sin(8𝑑 NOUN iajs-2703 118 10 ) ) PUNCT iajs-2703 119 1 + + CCONJ iajs-2703 119 2 cos(8𝑑 cos(8𝑑 NOUN iajs-2703 119 3 ) ) PUNCT iajs-2703 119 4 , , PUNCT iajs-2703 119 5 and and CCONJ iajs-2703 119 6 𝑀 𝑀 X iajs-2703 119 7 = = SYM iajs-2703 119 8 8 8 NUM iajs-2703 119 9 . . PUNCT iajs-2703 119 10 problem problem NOUN iajs-2703 119 11 3 3 NUM iajs-2703 119 12 : : PUNCT iajs-2703 119 13 [ [ X iajs-2703 119 14 15 15 NUM iajs-2703 119 15 ] ] PUNCT iajs-2703 119 16 𝑒1 𝑒1 PROPN iajs-2703 119 17 β€²β€²(𝑑 β€²β€²(𝑑 PROPN iajs-2703 119 18 ) ) PUNCT iajs-2703 119 19 + + SYM iajs-2703 119 20 𝑒1(𝑑 𝑒1(𝑑 SYM iajs-2703 119 21 ) ) PUNCT iajs-2703 119 22 = = NOUN iajs-2703 119 23 0.001 0.001 NUM iajs-2703 119 24 cos(𝑑 cos(𝑑 NOUN iajs-2703 119 25 ) ) PUNCT iajs-2703 119 26 , , PUNCT iajs-2703 119 27 𝑒1(0 𝑒1(0 PROPN iajs-2703 119 28 ) ) PUNCT iajs-2703 119 29 = = SYM iajs-2703 119 30 1 1 NUM iajs-2703 119 31 , , PUNCT iajs-2703 119 32 𝑒1 𝑒1 PROPN iajs-2703 119 33 β€² β€² NUM iajs-2703 119 34 ( ( PUNCT iajs-2703 119 35 0 0 NUM iajs-2703 119 36 ) ) PUNCT iajs-2703 119 37 = = SYM iajs-2703 119 38 0 0 NUM iajs-2703 119 39 , , PUNCT iajs-2703 119 40 𝑒2 𝑒2 PROPN iajs-2703 119 41 β€²β€²(𝑑 β€²β€²(𝑑 PROPN iajs-2703 119 42 ) ) PUNCT iajs-2703 119 43 + + PUNCT iajs-2703 119 44 𝑒2(𝑑 𝑒2(𝑑 PROPN iajs-2703 119 45 ) ) PUNCT iajs-2703 119 46 = = NOUN iajs-2703 119 47 0.001 0.001 NUM iajs-2703 119 48 sin(𝑑 sin(𝑑 PROPN iajs-2703 119 49 ) ) PUNCT iajs-2703 119 50 , , PUNCT iajs-2703 119 51 𝑒2(0 𝑒2(0 NOUN iajs-2703 119 52 ) ) PUNCT iajs-2703 119 53 = = SYM iajs-2703 119 54 0 0 NUM iajs-2703 119 55 , , PUNCT iajs-2703 119 56 𝑒2 𝑒2 PROPN iajs-2703 119 57 β€² β€² NUM iajs-2703 119 58 ( ( PUNCT iajs-2703 119 59 0 0 NUM iajs-2703 119 60 ) ) PUNCT iajs-2703 119 61 = = SYM iajs-2703 120 1 0.9995 0.9995 NUM iajs-2703 120 2 . . PUNCT iajs-2703 121 1 exact exact ADJ iajs-2703 121 2 solution solution NOUN iajs-2703 121 3 is be AUX iajs-2703 121 4 𝑒1(𝑑 𝑒1(𝑑 NOUN iajs-2703 121 5 ) ) PUNCT iajs-2703 121 6 = = SYM iajs-2703 121 7 cos(𝑑 cos(𝑑 X iajs-2703 121 8 ) ) PUNCT iajs-2703 121 9 +0.0005 +0.0005 NUM iajs-2703 121 10 𝑑 𝑑 PROPN iajs-2703 121 11 sin(𝑑 sin(𝑑 PROPN iajs-2703 121 12 ) ) PUNCT iajs-2703 121 13 , , PUNCT iajs-2703 121 14 𝑒2(𝑑 𝑒2(𝑑 PROPN iajs-2703 121 15 ) ) PUNCT iajs-2703 121 16 = = SYM iajs-2703 121 17 sin(𝑑 sin(𝑑 PROPN iajs-2703 121 18 ) ) PUNCT iajs-2703 121 19 βˆ’0.0005 βˆ’0.0005 NUM iajs-2703 121 20 𝑑 𝑑 PRON iajs-2703 121 21 cos(𝑑 cos(𝑑 PROPN iajs-2703 121 22 ) ) PUNCT iajs-2703 121 23 , , PUNCT iajs-2703 121 24 and and CCONJ iajs-2703 121 25 𝑀 𝑀 X iajs-2703 121 26 = = SYM iajs-2703 121 27 1 1 X iajs-2703 121 28 . . X iajs-2703 121 29 problem problem NOUN iajs-2703 121 30 4 4 NUM iajs-2703 121 31 : : PUNCT iajs-2703 122 1 [ [ X iajs-2703 122 2 16 16 NUM iajs-2703 122 3 ] ] PUNCT iajs-2703 122 4 𝑒′′(𝑑 𝑒′′(𝑑 NOUN iajs-2703 122 5 ) ) PUNCT iajs-2703 122 6 + + CCONJ iajs-2703 122 7 ( ( PUNCT iajs-2703 122 8 101 101 NUM iajs-2703 122 9 2 2 NUM iajs-2703 122 10 βˆ’ βˆ’ NUM iajs-2703 122 11 99 99 NUM iajs-2703 122 12 2 2 NUM iajs-2703 122 13 βˆ’ βˆ’ NUM iajs-2703 122 14 99 99 NUM iajs-2703 122 15 2 2 NUM iajs-2703 122 16 101 101 NUM iajs-2703 122 17 2 2 NUM iajs-2703 122 18 ) ) PUNCT iajs-2703 122 19 𝑒(𝑑 𝑒(𝑑 PROPN iajs-2703 122 20 ) ) PUNCT iajs-2703 122 21 = = PUNCT iajs-2703 123 1 ( ( PUNCT iajs-2703 123 2 93 93 NUM iajs-2703 123 3 2 2 NUM iajs-2703 123 4 cos(2𝑑 cos(2𝑑 X iajs-2703 123 5 ) ) PUNCT iajs-2703 124 1 βˆ’ βˆ’ PROPN iajs-2703 124 2 99 99 NUM iajs-2703 124 3 2 2 NUM iajs-2703 124 4 sin(2𝑑 sin(2𝑑 PUNCT iajs-2703 124 5 ) ) PUNCT iajs-2703 124 6 93 93 NUM iajs-2703 124 7 2 2 NUM iajs-2703 124 8 sin(2𝑑 sin(2𝑑 NUM iajs-2703 124 9 ) ) PUNCT iajs-2703 125 1 βˆ’ βˆ’ PROPN iajs-2703 125 2 99 99 NUM iajs-2703 125 3 2 2 NUM iajs-2703 125 4 cos(2𝑑 cos(2𝑑 NOUN iajs-2703 125 5 ) ) PUNCT iajs-2703 125 6 ) ) PUNCT iajs-2703 125 7 , , PUNCT iajs-2703 125 8 𝑒(0 𝑒(0 PROPN iajs-2703 125 9 ) ) PUNCT iajs-2703 125 10 = = PUNCT iajs-2703 126 1 ( ( PUNCT iajs-2703 126 2 0 0 NUM iajs-2703 126 3 1 1 NUM iajs-2703 126 4 ) ) PUNCT iajs-2703 126 5 , , PUNCT iajs-2703 126 6 𝑒′(0 𝑒′(0 NOUN iajs-2703 126 7 ) ) PUNCT iajs-2703 126 8 = = SYM iajs-2703 126 9 ( ( PUNCT iajs-2703 126 10 βˆ’10 βˆ’10 X iajs-2703 126 11 12 12 NUM iajs-2703 126 12 ) ) PUNCT iajs-2703 126 13 . . PUNCT iajs-2703 127 1 exact exact ADJ iajs-2703 127 2 solution solution NOUN iajs-2703 127 3 and and CCONJ iajs-2703 127 4 frequency frequency NOUN iajs-2703 127 5 are be AUX iajs-2703 127 6 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 127 7 ) ) PUNCT iajs-2703 127 8 = = SYM iajs-2703 127 9 ( ( PUNCT iajs-2703 127 10 βˆ’ βˆ’ NOUN iajs-2703 127 11 cos(10𝑑)(𝑑 cos(10𝑑)(𝑑 NOUN iajs-2703 127 12 ) ) PUNCT iajs-2703 127 13 βˆ’ βˆ’ PRON iajs-2703 127 14 sin(10𝑑 sin(10𝑑 NOUN iajs-2703 127 15 ) ) PUNCT iajs-2703 127 16 + + CCONJ iajs-2703 127 17 cos(2𝑑 cos(2𝑑 X iajs-2703 127 18 ) ) PUNCT iajs-2703 127 19 cos(10𝑑 cos(10𝑑 VERB iajs-2703 127 20 ) ) PUNCT iajs-2703 127 21 + + CCONJ iajs-2703 127 22 sin(10𝑑 sin(10𝑑 X iajs-2703 127 23 ) ) PUNCT iajs-2703 127 24 + + CCONJ iajs-2703 127 25 sin(2𝑑 sin(2𝑑 ADJ iajs-2703 127 26 ) ) PUNCT iajs-2703 127 27 ) ) PUNCT iajs-2703 127 28 , , PUNCT iajs-2703 127 29 𝑀 𝑀 X iajs-2703 127 30 = = SYM iajs-2703 127 31 10 10 NUM iajs-2703 127 32 . . PUNCT iajs-2703 127 33 problem problem NOUN iajs-2703 127 34 5 5 NUM iajs-2703 127 35 : : PUNCT iajs-2703 128 1 [ [ X iajs-2703 128 2 17 17 NUM iajs-2703 128 3 ] ] PUNCT iajs-2703 128 4 oscillatory oscillatory ADJ iajs-2703 128 5 system system NOUN iajs-2703 128 6 problem problem NOUN iajs-2703 128 7 𝑒′′(𝑑 𝑒′′(𝑑 VERB iajs-2703 128 8 ) ) PUNCT iajs-2703 129 1 + + CCONJ iajs-2703 129 2 ( ( PUNCT iajs-2703 129 3 13 13 NUM iajs-2703 129 4 βˆ’12 βˆ’12 NOUN iajs-2703 129 5 βˆ’12 βˆ’12 NOUN iajs-2703 129 6 13 13 NUM iajs-2703 129 7 ) ) PUNCT iajs-2703 129 8 𝑒(𝑑 𝑒(𝑑 PROPN iajs-2703 129 9 ) ) PUNCT iajs-2703 129 10 = = PUNCT iajs-2703 129 11 ( ( PUNCT iajs-2703 129 12 9 9 NUM iajs-2703 129 13 cos(2𝑑 cos(2𝑑 NOUN iajs-2703 129 14 ) ) PUNCT iajs-2703 130 1 βˆ’ βˆ’ PROPN iajs-2703 130 2 12 12 NUM iajs-2703 130 3 sin(2𝑑 sin(2𝑑 ADJ iajs-2703 130 4 ) ) PUNCT iajs-2703 130 5 βˆ’12 βˆ’12 PRON iajs-2703 131 1 cos(2𝑑 cos(2𝑑 NOUN iajs-2703 131 2 ) ) PUNCT iajs-2703 132 1 + + CCONJ iajs-2703 132 2 9 9 NUM iajs-2703 132 3 sin(2𝑑 sin(2𝑑 NUM iajs-2703 132 4 ) ) PUNCT iajs-2703 132 5 ) ) PUNCT iajs-2703 132 6 , , PUNCT iajs-2703 132 7 ibn ibn PROPN iajs-2703 132 8 al al PROPN iajs-2703 132 9 - - PUNCT iajs-2703 132 10 haitham haitham PROPN iajs-2703 132 11 jour jour X iajs-2703 132 12 . . PROPN iajs-2703 133 1 for for ADP iajs-2703 133 2 pure pure ADJ iajs-2703 133 3 & & CCONJ iajs-2703 133 4 appl appl PROPN iajs-2703 133 5 . . PUNCT iajs-2703 134 1 sci sci PROPN iajs-2703 134 2 . . PROPN iajs-2703 135 1 34(4)2021 34(4)2021 NUM iajs-2703 135 2 64 64 NUM iajs-2703 135 3 𝑒(0 𝑒(0 PROPN iajs-2703 135 4 ) ) PUNCT iajs-2703 135 5 = = PUNCT iajs-2703 135 6 ( ( PUNCT iajs-2703 135 7 1 1 NUM iajs-2703 135 8 0 0 NUM iajs-2703 135 9 ) ) PUNCT iajs-2703 135 10 , , PUNCT iajs-2703 135 11 𝑒′(0 𝑒′(0 NOUN iajs-2703 135 12 ) ) PUNCT iajs-2703 135 13 = = SYM iajs-2703 135 14 ( ( PUNCT iajs-2703 135 15 βˆ’4 βˆ’4 NOUN iajs-2703 135 16 8 8 NUM iajs-2703 135 17 ) ) PUNCT iajs-2703 135 18 . . PUNCT iajs-2703 136 1 exact exact ADJ iajs-2703 136 2 solution solution NOUN iajs-2703 136 3 and and CCONJ iajs-2703 136 4 frequency frequency NOUN iajs-2703 136 5 are be AUX iajs-2703 136 6 𝑒(𝑑 𝑒(𝑑 NOUN iajs-2703 136 7 ) ) PUNCT iajs-2703 136 8 = = SYM iajs-2703 136 9 ( ( PUNCT iajs-2703 136 10 sin(𝑑 sin(𝑑 PROPN iajs-2703 136 11 ) ) PUNCT iajs-2703 136 12 βˆ’ βˆ’ PROPN iajs-2703 136 13 sin(5𝑑 sin(5𝑑 NOUN iajs-2703 136 14 ) ) PUNCT iajs-2703 137 1 + + CCONJ iajs-2703 137 2 cos(2𝑑 cos(2𝑑 X iajs-2703 137 3 ) ) PUNCT iajs-2703 138 1 sin(𝑑 sin(𝑑 PROPN iajs-2703 138 2 ) ) PUNCT iajs-2703 138 3 + + NUM iajs-2703 138 4 sin(5𝑑 sin(5𝑑 NOUN iajs-2703 138 5 ) ) PUNCT iajs-2703 139 1 + + CCONJ iajs-2703 139 2 sin(2𝑑 sin(2𝑑 X iajs-2703 139 3 ) ) PUNCT iajs-2703 139 4 ) ) PUNCT iajs-2703 139 5 , , PUNCT iajs-2703 139 6 𝑀 𝑀 X iajs-2703 139 7 = = SYM iajs-2703 139 8 5 5 X iajs-2703 139 9 . . PUNCT iajs-2703 139 10 ( ( PUNCT iajs-2703 139 11 a a X iajs-2703 139 12 ) ) PUNCT iajs-2703 139 13 comparisons comparison NOUN iajs-2703 139 14 of of ADP iajs-2703 139 15 the the DET iajs-2703 139 16 methods method NOUN iajs-2703 139 17 ( ( PUNCT iajs-2703 139 18 i i NOUN iajs-2703 139 19 ) ) PUNCT iajs-2703 139 20 in in ADP iajs-2703 139 21 section section NOUN iajs-2703 139 22 4 4 NUM iajs-2703 139 23 . . PUNCT iajs-2703 139 24 ( ( PUNCT iajs-2703 139 25 b b X iajs-2703 139 26 ) ) PUNCT iajs-2703 139 27 comparisons comparison NOUN iajs-2703 139 28 of of ADP iajs-2703 139 29 the the DET iajs-2703 139 30 methods method NOUN iajs-2703 139 31 ( ( PUNCT iajs-2703 139 32 ii ii NOUN iajs-2703 139 33 ) ) PUNCT iajs-2703 139 34 in in ADP iajs-2703 139 35 section section NOUN iajs-2703 139 36 4 4 NUM iajs-2703 139 37 . . PUNCT iajs-2703 139 38 figure figure NOUN iajs-2703 139 39 1 1 NUM iajs-2703 139 40 . . PUNCT iajs-2703 140 1 the the DET iajs-2703 140 2 competence competence NOUN iajs-2703 140 3 curves curve VERB iajs-2703 140 4 for for ADP iajs-2703 140 5 problem problem NOUN iajs-2703 140 6 1 1 NUM iajs-2703 140 7 . . PUNCT iajs-2703 141 1 ( ( PUNCT iajs-2703 141 2 a a X iajs-2703 141 3 ) ) PUNCT iajs-2703 141 4 comparisons comparison NOUN iajs-2703 141 5 of of ADP iajs-2703 141 6 the the DET iajs-2703 141 7 methods method NOUN iajs-2703 141 8 ( ( PUNCT iajs-2703 141 9 i i NOUN iajs-2703 141 10 ) ) PUNCT iajs-2703 141 11 in in ADP iajs-2703 141 12 section section NOUN iajs-2703 141 13 4 4 NUM iajs-2703 141 14 ( ( PUNCT iajs-2703 141 15 b b NOUN iajs-2703 141 16 ) ) PUNCT iajs-2703 141 17 comparisons comparison NOUN iajs-2703 141 18 of of ADP iajs-2703 141 19 the the DET iajs-2703 141 20 methods method NOUN iajs-2703 141 21 ( ( PUNCT iajs-2703 141 22 ii ii NOUN iajs-2703 141 23 ) ) PUNCT iajs-2703 141 24 in in ADP iajs-2703 141 25 section section NOUN iajs-2703 141 26 4 4 NUM iajs-2703 141 27 . . PUNCT iajs-2703 141 28 figure figure NOUN iajs-2703 141 29 2 2 NUM iajs-2703 141 30 . . PUNCT iajs-2703 142 1 the the DET iajs-2703 142 2 competence competence NOUN iajs-2703 142 3 curves curve VERB iajs-2703 142 4 for for ADP iajs-2703 142 5 problem problem NOUN iajs-2703 142 6 2 2 NUM iajs-2703 142 7 . . PUNCT iajs-2703 143 1 ibn ibn PROPN iajs-2703 143 2 al al PROPN iajs-2703 143 3 - - PUNCT iajs-2703 143 4 haitham haitham PROPN iajs-2703 143 5 jour jour X iajs-2703 143 6 . . PROPN iajs-2703 143 7 for for ADP iajs-2703 143 8 pure pure ADJ iajs-2703 143 9 & & CCONJ iajs-2703 143 10 appl appl PROPN iajs-2703 143 11 . . PUNCT iajs-2703 144 1 sci sci PROPN iajs-2703 144 2 . . PROPN iajs-2703 145 1 34(4)2021 34(4)2021 NUM iajs-2703 145 2 65 65 NUM iajs-2703 145 3 ( ( PUNCT iajs-2703 145 4 a a PRON iajs-2703 145 5 ) ) PUNCT iajs-2703 145 6 comparisons comparison NOUN iajs-2703 145 7 of of ADP iajs-2703 145 8 the the DET iajs-2703 145 9 methods method NOUN iajs-2703 145 10 ( ( PUNCT iajs-2703 145 11 i i NOUN iajs-2703 145 12 ) ) PUNCT iajs-2703 145 13 in in ADP iajs-2703 145 14 section section NOUN iajs-2703 145 15 4 4 NUM iajs-2703 145 16 . . PUNCT iajs-2703 146 1 ( ( PUNCT iajs-2703 146 2 b b X iajs-2703 146 3 ) ) PUNCT iajs-2703 146 4 comparisons comparison NOUN iajs-2703 146 5 of of ADP iajs-2703 146 6 the the DET iajs-2703 146 7 methods method NOUN iajs-2703 146 8 ( ( PUNCT iajs-2703 146 9 ii ii NOUN iajs-2703 146 10 ) ) PUNCT iajs-2703 146 11 in in ADP iajs-2703 146 12 section section NOUN iajs-2703 146 13 4 4 NUM iajs-2703 146 14 . . PUNCT iajs-2703 146 15 figure figure VERB iajs-2703 146 16 3 3 NUM iajs-2703 146 17 . . PUNCT iajs-2703 147 1 the the DET iajs-2703 147 2 competence competence NOUN iajs-2703 147 3 curves curve VERB iajs-2703 147 4 for for ADP iajs-2703 147 5 problem problem NOUN iajs-2703 147 6 3 3 X iajs-2703 147 7 . . PUNCT iajs-2703 148 1 ( ( PUNCT iajs-2703 148 2 a a X iajs-2703 148 3 ) ) PUNCT iajs-2703 148 4 comparisons comparison NOUN iajs-2703 148 5 of of ADP iajs-2703 148 6 the the DET iajs-2703 148 7 methods method NOUN iajs-2703 148 8 ( ( PUNCT iajs-2703 148 9 i i NOUN iajs-2703 148 10 ) ) PUNCT iajs-2703 148 11 in in ADP iajs-2703 148 12 section section NOUN iajs-2703 148 13 4 4 NUM iajs-2703 148 14 . . PUNCT iajs-2703 149 1 ( ( PUNCT iajs-2703 149 2 b b X iajs-2703 149 3 ) ) PUNCT iajs-2703 149 4 comparisons comparison NOUN iajs-2703 149 5 of of ADP iajs-2703 149 6 the the DET iajs-2703 149 7 methods method NOUN iajs-2703 149 8 ( ( PUNCT iajs-2703 149 9 ii ii NOUN iajs-2703 149 10 ) ) PUNCT iajs-2703 149 11 in in ADP iajs-2703 149 12 section section NOUN iajs-2703 149 13 4 4 NUM iajs-2703 149 14 . . PUNCT iajs-2703 149 15 figure figure VERB iajs-2703 149 16 4 4 NUM iajs-2703 149 17 . . PUNCT iajs-2703 150 1 the the DET iajs-2703 150 2 competence competence NOUN iajs-2703 150 3 curves curve VERB iajs-2703 150 4 for for ADP iajs-2703 150 5 problem problem NOUN iajs-2703 150 6 4 4 NUM iajs-2703 150 7 . . PUNCT iajs-2703 151 1 ibn ibn PROPN iajs-2703 151 2 al al PROPN iajs-2703 151 3 - - PUNCT iajs-2703 151 4 haitham haitham PROPN iajs-2703 151 5 jour jour X iajs-2703 151 6 . . PROPN iajs-2703 151 7 for for ADP iajs-2703 151 8 pure pure ADJ iajs-2703 151 9 & & CCONJ iajs-2703 151 10 appl appl PROPN iajs-2703 151 11 . . PUNCT iajs-2703 152 1 sci sci PROPN iajs-2703 152 2 . . PROPN iajs-2703 153 1 34(4)2021 34(4)2021 NUM iajs-2703 153 2 66 66 NUM iajs-2703 153 3 ( ( PUNCT iajs-2703 153 4 a a PRON iajs-2703 153 5 ) ) PUNCT iajs-2703 153 6 comparisons comparison NOUN iajs-2703 153 7 of of ADP iajs-2703 153 8 the the DET iajs-2703 153 9 methods method NOUN iajs-2703 153 10 ( ( PUNCT iajs-2703 153 11 i i NOUN iajs-2703 153 12 ) ) PUNCT iajs-2703 153 13 in in ADP iajs-2703 153 14 section section NOUN iajs-2703 153 15 4 4 NUM iajs-2703 153 16 . . PUNCT iajs-2703 154 1 ( ( PUNCT iajs-2703 154 2 b b X iajs-2703 154 3 ) ) PUNCT iajs-2703 154 4 comparisons comparison NOUN iajs-2703 154 5 of of ADP iajs-2703 154 6 the the DET iajs-2703 154 7 methods method NOUN iajs-2703 154 8 ( ( PUNCT iajs-2703 154 9 ii ii NOUN iajs-2703 154 10 ) ) PUNCT iajs-2703 154 11 in in ADP iajs-2703 154 12 section section NOUN iajs-2703 154 13 4 4 NUM iajs-2703 154 14 . . PUNCT iajs-2703 154 15 figure figure VERB iajs-2703 154 16 5 5 NUM iajs-2703 154 17 : : PUNCT iajs-2703 154 18 the the DET iajs-2703 154 19 competence competence NOUN iajs-2703 154 20 curves curve VERB iajs-2703 154 21 for for ADP iajs-2703 154 22 problem problem NOUN iajs-2703 154 23 5 5 NUM iajs-2703 154 24 . . SYM iajs-2703 154 25 5 5 NUM iajs-2703 154 26 . . 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