×

The homotopy perturbation method for nonlinear oscillators with discontinuities. (English) Zbl 1039.65052

Summary: The homotopy perturbation method is applied to the nonlinear oscillators with discontinuities. Only one iteration leads to high accuracy of the solutions.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bender, C. M.; Pinsky, K. S.; Simmons, L. M., A new perturbative approach to nonlinear problems, Journal of Mathematical Physics, 30, 7, 1447-1455 (1989) · Zbl 0684.34008
[2] Andrianov, I.; Awrejcewicz, J., Construction of periodic solution to partial differential equations with nonlinear boundary conditions, International Journal of Nonlinear Sciences and Numerical Simulation, 1, 4 (2000) · Zbl 1237.34050
[3] He, J. H., A note on delta-perturbation expansion method, Applied Mathematics and Mechanics, 23, 6, 634-638 (2002) · Zbl 1029.34043
[4] Liao, S. J., Homotopy analysis method: a new analytic method for nonlinear problems, Applied Mathematics and Mechanics (English-Ed.), 19, 10, 957-962 (1998) · Zbl 1126.34311
[5] J.H. He, Comparison of Homotopy Perturbation Method and Homotopy Analysis Method, International Congress of Mathematicians, Beijing, 20-28 August, 2002; J.H. He, Comparison of Homotopy Perturbation Method and Homotopy Analysis Method, International Congress of Mathematicians, Beijing, 20-28 August, 2002
[6] He, J. H., Variational iteration method: a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34, 4, 699-708 (1999) · Zbl 1342.34005
[7] He, J. H., Bookkeeping parameter in perturbation methods, International Journal of Non-Linear Sciences and Numerical Simulation, 2, 3, 257-264 (2001) · Zbl 1072.34508
[8] He, J. H., A review on some new recently developed nonlinear analytical techniques, International Journal of Nonlinear Sciences and Numerical Simulation, 1, 1, 51-70 (2000) · Zbl 0966.65056
[9] Nayfeh, A. H., Introduction to Perturbation Techniques (1981), John Wiley & Sons: John Wiley & Sons New York · Zbl 0449.34001
[10] He, J.-H., An approximate solution technique depending upon an artificial parameter, Communications in Nonlinear Science and Numerical Simulation, 3, 2, 92-97 (1998) · Zbl 0921.35009
[11] He, J. H., Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 3/4, 257-262 (1999) · Zbl 0956.70017
[12] He, J. H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics, 35, 1, 37-43 (2000) · Zbl 1068.74618
[13] He, J. H., Gongcheng Yu Kexue zhong de jinshi feixianxing feixi fangfa (in Chinese), Asymptotic Methods In Engineering and Sciences (2002), Henan Science and Technology Press: Henan Science and Technology Press Zhengzhou · Zbl 1021.34001
[14] He, J. H., A modified perturbation technique depending upon an artificial parameter, Meccanica, 35, 299-311 (2000) · Zbl 0986.70016
[15] He, J. H., Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: expansion of a constant, International Journal of Non-Linear Mechanics, 37, 2, 309-314 (2002) · Zbl 1116.34320
[16] He, J. H., Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part II: a new transformation, International Journal of Non-Linear Mechanics, 37, 2, 315-320 (2002) · Zbl 1116.34321
[17] He, J. H., Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part III: double series expansion, International Journal of Non-Linear Sciences and Numerical Simulation, 2, 4, 317-320 (2001) · Zbl 1072.34507
[18] Acton, J. R.; Squire, P. T., Solving Equations with Physical Understanding (1985), Adam Hilger Ltd: Adam Hilger Ltd Bristol
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.