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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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