Semi-analytical iteration techniques for solving differential equations

Altaie, Huda Omran; Ali, Adel Rashed A.; Huisen, Reem Waleed

doi:10.47974/JIM-1756

Open Access Research Article

Semi-analytical iteration techniques for solving differential equations

^*Huda Omran AltaieCorresponding authorhuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BaghdadBaghdad, IraqView full profile → , Adel Rashed A. Aliadil.r.a@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BaghdadBaghdad, IraqView full profile → , Reem Waleed Huisenreem.w.h@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 715–719Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1756XML

Received:: 17 Oct 2023
Published Online:: 31 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1756
Pages:: 715–719

Abstract

The main objective of this work is to use and compare some techniques, namely the variational Iteration method (VIM), Decomposition Method (ADM), Differential Transform Method (DTM), and Temimi and Ansari Method (TAM) for differential equations of the first and second orders that appeared in physics and engineering. Notably, the results indicate that the VIM gives a solution in series form, which converges to an exact solution;. At the same time, DTM is easy to apply but requires transformation, ADM does not need any transformation except the calculation of Adomain polynomials. TAM solved nonlinear problems in much easier iteration steps, which converge to the true solution without applying any assumption. The results obtained converge rapidly to the exact solution.

Keywords

A domain decomposition method Series solution Differential equations Temimi and Ansari method

Subject Classifications

12H2031B35

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