Approximate solutions of nonlinear partial differential equations by modified q -homotopy analysis method

Abstract

A modified q -homotopy analysis method (m q -HAM) was proposed for solving n th-order nonlinear differential equations. This method improves the convergence of the series solution in the n HAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting the n th-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed. © 2013 Shaheed N. Huseen and Said R. Grace.