Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 37, Issue 2, Pages 315-320Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0020-7462(00)00117-7
Keywords
perturbation method; non-linear equation; Duffing equation; van der Pol equation; Lindstedt-Poincare method
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In this paper, a modified Lindstedt-Poincare method is proposed. In this technique, we introduce a new transformation of the independent variable. This transformation will also allow us to avoid the occurrence of secular terms in the perturbation series solution, Some examples are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weakly non-linear systems. but also for strongly non-linear systems. (C) 2001 Elsevier Science Ltd. All rights reserved.
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