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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.

34A36Discontinuous equations
34E05Asymptotic expansions (ODE)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34C15Nonlinear oscillations, coupled oscillators (ODE)
Full Text: DOI
[1] Bender, C. M.; Pinsky, K. S.; Simmons, L. M.: A new perturbative approach to nonlinear problems. J. math. Phys. 30, No. 7, 1447-1455 (1989) · Zbl 0684.34008
[2] Andrianov, I.; Awrejcewicz, J.: Construction of periodic solution to partial differential equations with nonlinear boundary conditions. Int. J. Nonlinear sci. Numer. simul. 1, No. 4 (2000) · Zbl 0977.35031
[3] He, J. H.: A note on delta-perturbation expansion method. Appl. math. Mech. 23, No. 6, 634-638 (2002) · Zbl 1029.34043
[4] He, J. H.: Homotopy perturbation technique. Comput. methods appl. Mech. eng. 178, No. 3--4, 257-262 (1999) · Zbl 0956.70017
[5] He, J. H.: A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear mech. 35, No. 1, 37-43 (2000) · Zbl 1068.74618
[6] He, J. H.: Variational iteration method: a kind of nonlinear analytical technique: some examples. Int. J. Nonlinear mech. 34, No. 4, 699-708 (1999) · Zbl 05137891
[7] He, J. H.: Bookkeeping parameter in perturbation methods. Int. J. Nonlinear sci. Numer. simul. 2, No. 3, 257-264 (2001) · Zbl 1072.34508
[8] He, J. H.: Preliminary report on the energy balance for nonlinear oscillations. Mech. res. Commun. 29, No. 2--3, 107-111 (2002) · Zbl 1048.70011
[9] He, J. H.: Determination of limit cycles for strongly nonlinear oscillators. Phys. rev. Lett. 90, No. 17, 174301 (2003)
[10] He, J. H.: A review on some new recently developed nonlinear analytical techniques. Int. J. Nonlinear sci. Numer. simul. 1, No. 1, 51-70 (2000) · Zbl 0966.65056
[11] He, J. H.: The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. math. Comput. 151, 287-292 (2004) · Zbl 1039.65052
[12] He, J. H.: Modified Lindstedt--Poincarè methods for some strongly nonlinear oscillations. Part I: Expansion of a constant. Int. J. Nonlinear mech. 37, No. 2, 309-314 (2002) · Zbl 1116.34320
[13] He, J. H.: Modified Lindstedt--Poincarè methods for some strongly nonlinear oscillations. Part II: A new transformation. Int. J. Nonlinear mech. 37, No. 2, 315-320 (2002) · Zbl 1116.34321
[14] He, J. H.: Modified Lindstedt--Poincarè methods for some strongly nonlinear oscillations. Part III: Double series expansion. Int. J. Nonlinear sci. Numer. simul. 2, No. 4, 317-320 (2001) · Zbl 1072.34507