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Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt–Poincaré method. (English) Zbl 1078.34509
The author considers a modified Lindstedt-Poincaré method for the study of a Cauchy problem for a nonlinear oscillator with jumping discontinuities. The main idea of the method is the introduction of an artificial small parameter in the equation which allows asymptotic expansions of the solution and of the frequency. At least for the presented problem, the high efficiency of the method is shown.
MSC:
34A36Discontinuous equations
34E05Asymptotic expansions (ODE)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34C15Nonlinear oscillations, coupled oscillators (ODE)