Study of convergence of homotopy perturbation method for systems of partial differential equations

Abstract

The aim of this paper is convergence study of homotopy perturbation method for systems of nonlinear partial differential equations. The sufficient condition for convergence of the method is addressed. Since mathematical modeling of numerous scientific and engineering experiments lead to Brusselator and Burgers’ system of equations, it is worth trying new methods to solve these systems. We construct a new efficient recurrent relation to solve nonlinear Burgers’ and Brusselator systems of equations. Comparison of the results obtained by homotopy perturbation method with those of Adomian’s decomposition method and dual-reciprocity boundary element method leads to significant consequences. Two standard problems are used to validate the method.