On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method

In the present work, we use the homotopy perturbation method (HPM) to solve the Newell- Whitehead-Segel non-linear differential equations. Four case study problems of Newell-Whitehead- Segel are solved by the HPM and the exact solutions are obtained. The trend of the rapid convergence of the sequences constructed by the method toward the exact solution is shown numerically. As a result the rapid convergence towards the exact solutions of HPM indicates that, using the HPM to solve the Newell-Whitehead-Segel non-linear differential equations, a reasonable less amount of computational work with acceptable accuracy may be sufficient. Moreover the application of the HPM proves that the method is an effective and simple tool for solving the Newell-Whitehead-Segel non-linear differential equations.

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