Solutions of random ordinary differential equations with laplace transform - Adomian decomposition method

Salman, Oras Abbas; Altaie, Huda Omran

doi:10.47974/JIM-1883

Open Access Research Article

Solutions of random ordinary differential equations with laplace transform - Adomian decomposition method

Oras Abbas Salmanoras.Abbas2203m@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.com huda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile →

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pp. 857–863Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1883XML

Received:: 16 Jan 2024
Published Online:: 30 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1883
Pages:: 857–863

Abstract

Combine the Laplace Adomian Decomposition method (LTADM) for non-linear random ordinary differential equations is utilised in a novel way to obtain accurate solutions.The iterative implementation of the Laplace transform decomposition is employed to approximate the solutions of ordinary differential equations with random components. We use a Normal distribution to analyse the parameters and initial conditions of ordinary differential equations with random components. Using the Mathematica 13.3 programme, the graphs of the approximate solutions and absolute error are presented. An investigation is conducted into the effects of the normal distribution on the results of random component differential equations. According to the results of the numerical investigations, this method is extremely effective. 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 differential equations in order to demonstrate its efficacy and potential.

Keywords

Laplace transform Random differential equations Normal distribution Semi analytic approach Decomposition technique

Subject Classifications

35R4535R70

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