an:02170680
Zbl 1072.34507
He, Jihuan
Modified Lindstedt-Poincar?? methods for some strongly nonlinear oscillations. III: Double series expansion
EN
Int. J. Nonlinear Sci. Numer. Simul. 2, No. 4, 317-320 (2001).
00080172
2001
j
34C15 34E05 34E10
Summary: We propose a new perturbation technique for strongly nonlinear oscillations with two parameters, which need not to be small in the present study. In this new method, the solution is expanded into a double series of the two parameters. In order to avoid the secular terms, a constant in the equation is also expressed in a double series expansion. The preliminary study shows that the obtained approximate solutions are uniformly valid on the whole solution domain.
For Part I: Expansion of a constant see Int. J. Non-Linear Mech. 37, No. 2, 309--314 (2002; Zbl 1116.34320); and Part II: A new transformation, ibid. 37, No. 2, 315--320 (2002; Zbl 1116.34321).
Zbl 1116.34320; Zbl 1116.34321