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Zbl 1015.70019
He, Jihuan
Iteration perturbation method for strongly nonlinear oscillations.
(English)
[J] J. Vib. Control 7, No.5, 631-642 (2001). ISSN 1077-5463; ISSN 1741-2986/e

Summary: We propose a perturbation technique coupling with iteration method, yielding a tool for an analytical solution of nonlinear equations of the form $u''+u+\varepsilon f(u,u')=0$, $u(0)=A$, $u'(0)=0$. The results obtained are valid not only for weakly nonlinear problems, but also for strongly nonlinear problems. Furthermore, the approximate solutions are valid for the whole solution domain, and even the first-step iteration leads to high accuracy. Some examples are given to illustrate the effectiveness of the method.
MSC 2000:
*70K60 General perturbation schemes

Keywords: iteration perturbation method; nonlinear oscillation; analytical solution

Cited in: Zbl 1106.70014

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