Efficient Numerical Method for Generating Closed Form Solution for Nonlinear Bratu Differential Equations

Abstract

This study presents a numerical solution of the Bratu differential equations (BDE) using the Sumudu transform series decomposition technique (STSDT). The process combines the Adomian polynomials (AP), series expansion (SE), and Sumudu transform (ST), and it ultimately converges perfectly to the exact solution. Examining four test problems demonstrates that the strategy converges more effectively than the literature-based approach. Calculations were performed using Maple 2022 software.