Analytical solutions of random integro differential equations by new combination Sumudu transform with ADM

Kaled, Ayman; Altaie, Huda Omran

doi:10.47974/JIM-2545

Open Access Research Article

Analytical solutions of random integro differential equations by new combination Sumudu transform with ADM

^*Ayman KaledCorresponding authorayman.saleh2303@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, 10071, IraqView full profile → , Huda Omran Altaiehuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BaghdadBaghdad, 10071, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1567–1571Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2545XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2545
Pages:: 1567–1571

Abstract

A new transform Sumudu Adomian Decomposition method (STADM) for non-linear random ordinary differential equations and the non-linear Random Integro differential equation (NRIDE) are utilized in a novel way to obtain accurate solutions. The iterative implementation of the coupled transform decomposition be use to approximated solution to ordinary differentials equation with random components. We use a normal distribution to analyze the parameters and initial conditions of ordinary differential equations with random components. Using Mathematica 13.3, the graphs of the approximate solutions and the absolute error are presented. An investigation is conducted into the effects of the normal distribution on the results of random component differential equations. Based on the numerical results, this method is highly effective. Some applications are presented as examples of how the proposed technique can be utilized to obtain analytical or numerical solutions to certain kinds of random differential equations, thereby demonstrating its efficacy and potential.

Keywords

Sumudu transform Analytical technique Random differential equation Ordinary differential equation

Subject Classifications

35R1135R60

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