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Momani, Shaher; Erjaee, G. H.; Alnasr, M. H.

The modified homotopy perturbation method for solving strongly nonlinear oscillators. (English) Zbl 1189.65168

Comput. Math. Appl. 58, No. 11-12, 2209-2220 (2009).
Summary: We propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé 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.

Cited in 18 Documents

MSC:

65L99 Numerical methods for ordinary differential equations

Keywords:

nonlinear oscillator; homotopy perturbation method; Laplace transform; Padé approximants
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\textit{S. Momani} et al., Comput. Math. Appl. 58, No. 11--12, 2209--2220 (2009; Zbl 1189.65168)
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References:

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