On convergence and error analysis of the parametric iteration method

Abstract

Parametric iteration method falls under the category of the analytic approximate methods for solving various kinds of nonlinear differential equations. Its convergence only for some special problems has been proved. However in this paper, an analysis of error is presented, then due to it, the convergence of method for general problems is proved. To assess the performance of the claimed error bound and also the convergence of the method, numerical experiments are presented performed in MATLAB 2012b.