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He’s parameter-expanding methods for strongly nonlinear oscillators. (English) Zbl 1120.65084
Summary: Ji-Huan He’s work [Int. J. Nonlinear Sci. Numer. Simul. 2, No. 3, 257–264 (2001; Zbl 1072.34508); Int. J. Non-Linear Mech. 37, No. 2, 309–314 (2002; Zbl 1116.34320)] on asymptotic techniques is briefly reviewed, and his parameter-expanding methods including the modified Lindstedt-Poincare method and the bookkeeping parameter method are discussed in detail. Some remarkable virtues of the methods are exploited, and their applications are illustrated.
MSC:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general