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

Authors:
E. Babolian;A. Azizi;J. Saeidian
Affiliations:
Department of Mathematics and Computer Sciences, Tarbiat Moallem University, 599 Taleghani Avenue, Tehran 1561836314, Iran;Department of Mathematics and Computer Sciences, Tarbiat Moallem University, 599 Taleghani Avenue, Tehran 1561836314, Iran;Department of Mathematics and Computer Sciences, Tarbiat Moallem University, 599 Taleghani Avenue, Tehran 1561836314, Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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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 v"0 in the homotopy equation. Examples assuring the efficiency and convenience of the suggested homotopy equation are comparatively presented.