An efficient approximate method for solving Bratu’s boundary value problem

Abstract

We compute the numerical solution of Bratu’s boundary value problem (BVP). To achieve this, we apply a new and useful approach to solve Bratu’s boundary value problem by using Green’s function and a new integral operator, along with a modified version of the Adomian decomposition method. This process produces solutions that call for the boundary conditions to be applied explicitly. Statistical results demonstrating the robustness and efficiency of the proposed scheme are included. An exact and approximate solution comparison is made with known results. The quantitative outcomes showcase our novel approach’s high numerical precision and consistency across a range of parameter configurations.