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Iteration perturbation method for strongly nonlinear oscillations. (English) Zbl 1015.70019

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:

70K60 General perturbation schemes for nonlinear problems in mechanics
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