Linearized perturbation technique and its applications to strongly nonlinear oscillators.(English)Zbl 1035.65070

Summary: A new perturbation technique called linearized perturbation method is proposed. Contrary to the traditional perturbation techniques, the unperturbed equations is obtained by linearizing the original nonlinear equation, not by setting $$\varepsilon = 0$$. Therefore, the obtained results are valid not only for small parameter, but also for very large values of $$\varepsilon$$. The present theory is processed as simple as the straightforward expansion, while omits the secular terms completely.

MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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References:

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