Approximate Solutions of Nonlinear Partial Differential Equations by Modified q -Homotopy Analysis Method
Shaheed N. Huseen, Said R. Grace
Source 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.
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