Abstract
A modified -homotopy analysis method (m-HAM) was proposed for solving th-order nonlinear differential equations. This method improves the convergence of the series solution in the HAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting the th-order nonlinear differential equation in the form of first-order differential equations. The solution of these 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.
Citation
Shaheed N. Huseen. Said R. Grace. "Approximate Solutions of Nonlinear Partial Differential Equations by Modified -Homotopy Analysis Method." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/569674