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

• Published in: Journal of interdisciplinary mathematics Vol. 27; no. 4; pp. 857 - 863
• Main Authors: Salman, Oras Abbas, Altaie, Huda Omran
• Format: Journal Article
• Language: English
• Published: 2024
• ISSN: 0972-0502; 2169-012X
• DOI: 10.47974/JIM-1883

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.