The modified homotopy perturbation method for solving strongly nonlinear oscillators

Authors:
Shaher Momani;G. H. Erjaee;M. H. Alnasr
Affiliations:
Department of Mathematics, Mutah University, P.O. Box: 7, Al-Karak, Jordan;Department of Mathematics and Physics, Qatar University, Doha, Qatar;Department of Mathematics and Physics, Qatar University, Doha, Qatar
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Pade approximants. This modified homotopy perturbation method (MHPM) utilizes an alternative framework to capture the periodic behavior of the solution, which is characteristic of oscillator equations, and to give a good approximation to the true solution in a very large region. The current results are compared with those derived from the established Runge-Kutta method in order to verify the accuracy of the MHPM. It is shown that there is excellent agreement between the two sets of results. Results also show that the numerical scheme is very effective and convenient for solving strongly nonlinear oscillators.