Comparison of Optimal Homotopy Asymptotic Method and Homotopy Perturbation Method for Improved Boussinesq Equation

Today nonlinear phenomenons play an important role in applied mathematics, physics and engineering. Explicit solutions of nonlinear partial differential equations sound essential in most caces. In homotopy method, without converting or linearization and by applying homotopy technique in topology, a homotopy with embedded parameters of p Î[0,1] can be created. In this paper, the improved Boussinesq equation will be solved by two methods: homotopy perturbation method and optimal homotopy Asymptotic method. Finally, the results will be compared and evaluated with the numerical values obtained by these methods. It is shown that the results of the optimal homotopy asymptotic method are better than the homotopy perturbation method.

Keywords:

Optimal Homotopy Asymptotic Method(OHAM) , Homotopy Perturbation Method(HPM) , Improve Boussinesq equation