Analytical approximate solutions of random integro differential equations with laplace decomposition method

Salman, Oras Abbas; Altaie, Huda Omran

doi:10.47974/JIM-1910

Open Access Research Article

Analytical approximate solutions of random integro differential equations with laplace decomposition method

^*Oras Abbas SalmanCorresponding authororas.Abbas2203m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile → , Huda Omran Altaiehuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 907–912Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1910XML

Received:: 07 Feb 2024
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1910
Pages:: 907–912

Abstract

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, 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 (LTADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 programme, the graphs of the approximate solutions and consecutive error are presented. Two applications are presented as examples of how the proposed technique can be utilised to obtain analytical or numerical solutions for certain kinds of Random Integro Differential Equations (RIDEs)in order to demonstrate its efficacy and potential.

Keywords

Laplace transform Random differential equations Integral equations Decomposition adomian technique Analytical technique

Subject Classifications

44A1044A20

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