In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein-Gordon and sine-Gordon equations. To present the present method's effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective.
In this article, the flow of liquid film over an unsteady elastic stretching surface is analyzed. Similarity transformations are used to transform the governing equations to a nonlinear ordinary differential equation. The differential equation reformulated to system of Voltera integral equations and solved analytically using the new technique of numerical solution called homotopy perturbation method. The results of the proposed method are compared with previously published work and the results are found to be in an excellent agreement. Also, discussed and presented graphically the effects of various parameters Darcy number and unsteadiness parameter.
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