A new approach to Bratu’s problem

摘要

In this paper, a Laplace transform decomposition numerical algorithm is introduced for solving Bratu’s problem. The numerical scheme is based on the application of Laplace transform integral operator to the differential equation. The nonlinear term is then decomposed and an iterative algorithm is constructed for the determination of the infinite series solution. The technique is illustrated with two numerical examples and the results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme.