Numerical Solution of Bratu-Type Initial Value Problems by Aboodh Adomian Decomposition Method

Year 2023, Volume: 20 Issue: 2, 64 - 75, 01.11.2023

Olutunde Odetunde , Abiodun Ajani Abasss Taiwo , Sefiu Onitilo

Abstract

This study presents an efficient method for solving Bratu equations with an initial value problem. The procedure is based on the use of Aboodh transform and Adomian decomposition method. Adomian polynomials for the index n replace the nonlinear term. The dependent variable components are also replaced in the recurrence relation by their corresponding Aboodh transform components of the same index. Therefore, the nonlinear problem is solved directly without any linearization or discretization.
Examples are presented to show the effectiveness and validity of this method. The derived results are compared with the existing exact solution.

Keywords

Bratu equation, Aboodh transform, Adomian decomposition method

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