Iterative differential quadrature solutions for Bratu problem

A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu's problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.