ALGORITHM FOR SOLVING A GENERALIZED HIROTA-SATSUMA COUPLED KDV EQUATION USING HOMOTOPY PERTURBATION TRANSFORM METHOD

摘要

In this paper, we merge homotopy perturbation method with He’s polynomials and Laplace transformation method to produce a highly effective algorithm for finding approximate solutions for generalized Hirota-Satsuma Coupled KdV equations. This technique is called the Homotopy Perturbation Transform Method (HPTM). With this technique, the solutions are obtained without any discretization or restrictive assumptions, and devoid of round-off errors. This technique solved a generalized Hirota-Satsuma Coupled KdV equation without using Adomian’s polynomials which can be considered as a clear advantage over the decomposition method. MAPLE software was used to calculate the series generated from the algorithm. The results reveal that the homotopy perturbation transform method (HPTM) is very efficient, simple and can be applied to other nonlinear problems.