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Nonperturbative (but approximate) method for solving differential equations and finding limit cycles. (English) Zbl 1051.65505

Summary: A nonperturbative method for solving differential equations and for finding limit cycles is proposed and is illustrated on the anharmonic oscillator and on the Van der Pol equation. It is shown to give the amplitude, period, and equation of the limit cycle with a better accuracy than any perturbative results so far obtained.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:

[1] Y. Yan Qian, in: Theory of Limit Cycles (1986)
[2] C.M. Andersen, SIAM J. Appl. Math 42 pp 678– (1982) · Zbl 0494.65053
[3] M.B. Dadfar, SIAM J. Appl. Math. 44 pp 881– (1984) · Zbl 0568.65048
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