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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 |

### Keywords:

Artificial parameter; Strongly nonlinear equations; numerical examples; linearized perturbation method
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\textit{J.-H. He}, Comput. Math. Appl. 45, No. 1--3, 1--8 (2003; Zbl 1035.65070)

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### References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.