id author title date pages extension mime words sentence flesch summary cache txt cana-5406 Rohit Nagargoje, Avinash Khambayat The Numerical Solutions of Partial Differential Equations using Two-Three-Dimensions Differential Transform Method 2025 10 .pdf application/pdf 3301 251 72 βˆ’ 1)(π‘˜ βˆ’ 𝛼 + 1)π‘ˆ(π‘˜ βˆ’ 𝛼 + 1, β„Ž) βˆ’ π‘˜ 𝛼=0 𝛿(π‘˜ βˆ’ 1) 𝑠𝑖𝑛 ( β„Žπœ‹ 2 ) β„Ž! βˆ’βˆ‘βˆ‘( 1 𝛽 )( 𝑠𝑖𝑛 ( (β„Ž βˆ’ 𝛽 βˆ’ 𝑠)πœ‹ 2 ) (β„Ž βˆ’ 𝛽)! Theorem 3: If 𝑧(𝑝1, 𝑝2… , π‘π‘š) = 𝑝1 β„Ž1 , 𝑝2 β„Ž2β€¦π‘π‘š β„Žπ‘š then, 𝑍(π‘˜1, π‘˜2… , π‘˜π‘š) = 𝛿(π‘˜1 βˆ’ β„Ž1)𝛿(π‘˜2 βˆ’ β„Ž2)…𝛿(π‘˜π‘š βˆ’ β„Žπ‘š) where, 𝛿(π‘˜π‘– βˆ’ β„Žπ‘–) = { 1 0 π‘˜π‘– = β„Žπ‘– π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’ Theorem 4: If 𝑧(𝑝1, 𝑝2… , π‘π‘š) = 𝑝1 β„Ž1 , 𝑝2 β„Ž2…sin(π‘Žπ‘₯𝑖 + 𝑏)β€¦π‘π‘š β„Žπ‘š π‘‘β„Žπ‘’π‘› 𝑍(π‘˜1, π‘˜2… , π‘˜π‘š) = 𝛿(π‘˜1 βˆ’ π‘˜2) cache/cana-5406.pdf txt/cana-5406.txt