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Zbl 1154.65349
Beléndez, A.; Pascual, C.; Beléndez, T.; Hernández, A.
Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He's homotopy perturbation method. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 1, 416-427 (2009). ISSN 1468-1218

Summary: He's homotopy perturbation method has been adapted to calculate higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term is an anti-symmetric and quadratic term. We find that He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Just one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 0.73\% for all values of oscillation amplitude, while this relative error is as low as 0.040\% when the second iteration is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance method reveals that the former is very effective and convenient.

MSC 2000:: *65L99 Numerical methods for ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: nonlinear oscillator; approximate solutions; homotopy perturbation method

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Zentralblatt MATH Berlin [Germany]