Approximate Solution of Linear and Nonlinear Partial Differential Equations Using Picard’s Iterative Method
DOI:
https://doi.org/10.31642/JoKMC/2018/110110%20Keywords:
Picard’s Iterative Method (PIM), linear partial differential equations (LPDEs), nonlinear Partial Differential Equations(NLPDEs).Abstract
This work discusses a new description of Picard’s iterative method (PIM) to get the approximate or sometimes exact solution of (linear and nonlinear) partial differential equations ,Provided that by examples to illustrate the reliability and ease of this method.
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Ogunfiditimi,F.O., “Numerical Solution Of Delay Differential Equations Using The Adomian Decomposition Method (ADM) ”, The International Journal Of Engineering And Science(IJES),Volume 4 , Issue 5, pages 18-23, 2015.
Ji-Huan He, “Homotopy perturbation method: a new nonlinear analytical technique”, Applied Mathematics and Computation 135(1), 73-79, 2003.
Ji-Huan He , Xu-Hong Wu, “Variational iteration method: New development and applications”, An International Journal Computers and Mathematics with Applications 54(2007) 881-894.
H.Temimi , A.R.Ansari, “A semi-analytical iterative technique for solving nonlinear problems”, Computers and Mathematics with Applications 61(2011)203-210.
Shatha Jabbar Mohammed, Maha A. Mohammed, “Mean Latin Hypercube Runge – Kutta Method to Solve the Influenza Model”, Iraqi Journal of Science, 2022, Vol.63, No.3, pp: 1158-1177.
Christopher C. Tisdell, “On Picard’s Iteration method to solve differential equations and a pedagogical space for otherness”, International Journal of Mathematical Education in Science and Technology, Volume 50, Issue 5,788-799,2019.
M. A. AL-Jawary, “Exact Solutions to linear and nonlinear wave and diffusion equations”, International Journal of Applied Mathematical Research, 4 (1) (2015) 106-118.
S.S.Nourazar, M.Soori and A. Nazari-Golshan, “On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method”, Australian Journal of Basic and Applied Sciences, 5(8):1400-1411, 2011.
Samaher Marez Yassein, Asmaa Abd Aswhad, “Efficient Iterative Method for solving Korteweg-de Vries Equations”, Iraqi Journal of Science, 2019, Vol.60, No.7, pp:1575-1583.
Asmaa A. Aswhad, Samaher M. Yassein, “Sumudu Iterative Method for solving Nonlinear Partial Differential Equations ” , Ibn Al-Haitham Jour. For pure & Appl. Sci. 34(2) 2021.
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