Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

الملخص EN

A modified q-homotopy analysis method (mq-HAM) was proposed for solving nth-order nonlinear differential equations.

This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012).

The proposed method provides an approximate solution by rewriting the nth-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.