id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cuesj-43	Hasan, Talaat I.	Cooperating Newton’s Method with Series Solution Method for Solving System of Linear Mixed Volterra-Fredholm Integral Equation of the Second Kind	2019	7	.pdf	application/pdf	3822	187	71	i q i u x u x u x u x T f x ∫∫ + + + + = α α α α0 0 1 1 2 2( ) ( ) ( ) ... (Source: Created by researcher) AQ1 b a Hasan: Cooperating Newton’s Method with Series Solution Method 30 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2019, 3 (1): 27-33 Solution: Let u x u xm m m q 1 1 1 0 ( ) ( )= = ∑ Then, using SSM, obtaining the values of coefficients a10=−2, a11=−2, a12=−1, a13=−0.3333, a14=−0.083333 and a15=−0.03333, For u x u xm m m q 2 2 2 0 ( ) ( )= = ∑ Then, using SSM, obtaining the values of coefficients a20=0, a21=−2, a22=−2, a23=−1, a24=−0.33333 and a25=−0.08333 Example (2): Solve LSMVFIE-2 �� ( ) ( ) sin( ) ( )(sin( ) cos( )) u x x x x x t t u dtdx x 1 2 2 0 0 2 2 2= − − + − ∫ ∫  �� ( ) ( ) cos( ) ( )(sin( ) cos( )) u x x x x t t t u dtdx x 2 10 0 2 2= − − + − ∫ ∫  Using SSM, where the exact solutions u1(x)=−2sin(x) and u2(x)=−2cos(x)?	cache/cuesj-43.pdf	txt/cuesj-43.txt