Journal of Applied Mathematics

An Optimal Iteration Method for Strongly Nonlinear Oscillators

Vasile Marinca and Nicolae Herişanu

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We introduce a new method, namely, the Optimal Iteration Perturbation Method (OIPM), to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solutions. The main advantage of this approach consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. A very good agreement was found between approximate and numerical solutions, which prove that OIPM is very efficient and accurate.

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J. Appl. Math., Volume 2012 (2012), Article ID 906341, 11 pages.

First available in Project Euclid: 17 October 2012

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Marinca, Vasile; Herişanu, Nicolae. An Optimal Iteration Method for Strongly Nonlinear Oscillators. J. Appl. Math. 2012 (2012), Article ID 906341, 11 pages. doi:10.1155/2012/906341.

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