A New Result On Adomian Decomposition Method For Solving Bratu’s Problem

Abstract

This paper investigates the properties of solution to the nonlinear Bratu’s problem. Approximate solution of the strongly nonlinear problem is obtained using the rapidly convergent Adomian decomposition method. The result shows that the problem has two solutions, bifurcated and has no solution depending on the value of the Frank-Kameneskii parameter. Of particular interest is the determination of the bifurcation point using Adomian decomposition method.

Keywords: nonlinear eigenvalue problem, rational function, Adomian decomposition method, Bratu’s problem.