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

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.