Some notes on using the homotopy perturbation method for solving time-dependent differential equations

https://doi.org/10.1016/j.mcm.2009.03.003Get rights and content
Under an Elsevier user license
open archive

Abstract

Although attempts have been made to solve time-dependent differential equations using homotopy perturbation method (HPM), none of the researchers have provided a universal homotopy equation. In this paper, going one step forward, we intend to make some guidelines for beginners who want to use the homotopy perturbation technique for solving their equations. These guidelines are based on the L part of the homotopy equation and the initial guess. Afterwards, for solving time-dependent differential equations, we suggest a universal L and v0 in the homotopy equation. Examples assuring the efficiency and convenience of the suggested homotopy equation are comparatively presented.

Keywords

Homotopy perturbation method
Klein–Gordon equations
Emden–Fowler equations
Evolution equations
Cauchy reaction-diffusion equations

Cited by (0)