Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part II: a new transformation

In this paper, a modified Lindstedt-Poincare method is proposed. In this te chnique, we introduce a new transformation of the independent variable. Thi s transformation will also allow us to avoid the occurrence of secular term s in the perturbation series solution, Some examples are given here to illu strate its effectiveness and convenience. The results show that the obtaine d approximate solutions are uniformly valid on the whole solution domain, a nd they are suitable not only for weakly non-linear systems. but also for s trongly non-linear systems. (C) 2001 Elsevier Science Ltd. All rights reser ved.