Analytical solutions via coupled Elzaki adomian decomposition method for some applications

Mohammed, Asmaa Mustafa; Altaie, Huda Omran

doi:10.47974/JIM-1868

Open Access Research Article

Analytical solutions via coupled Elzaki adomian decomposition method for some applications

Asmaa Mustafa MohammedAsmaa.mostafa2203m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile → , ^*Huda Omran AltaieCorresponding authordr.huda_hm2019@yahoo.comDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile →

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pp. 761–766Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1868XML

Received:: 10 Jan 2024
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1868
Pages:: 761–766

Abstract

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (ETADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 programme, the graphs of the approximate solutions are presented.

Keywords

Elzaki transform Decomposition technique Ordinary differential equations Iterative methods Analytical solution

Subject Classifications

49M2705C51

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