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2012 An Optimal Iteration Method for Strongly Nonlinear Oscillators
Vasile Marinca, Nicolae Herişanu
J. Appl. Math. 2012: 1-11 (2012). DOI: 10.1155/2012/906341


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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Vasile Marinca. Nicolae Herişanu. "An Optimal Iteration Method for Strongly Nonlinear Oscillators." J. Appl. Math. 2012 1 - 11, 2012.


Published: 2012
First available in Project Euclid: 17 October 2012

zbMATH: 1235.65098
MathSciNet: MR2861940
Digital Object Identifier: 10.1155/2012/906341

Rights: Copyright © 2012 Hindawi


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