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Volumn 8, Issue 2, 2007, Pages 243-248

A comparative study of He's Homotopy Perturbation Method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities

Author keywords

He's homotopy perturbation method; Nonlinear oscillators

Indexed keywords


EID: 34249884541     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2007.8.2.243     Document Type: Article
Times cited : (153)

References (37)
  • 4
    • 0003662274 scopus 로고
    • translated by WolframStadler, Clarendon Press, Oxford
    • Hagedorn, P. Nonlinear Oscillations (translated by WolframStadler), Clarendon Press, Oxford, 1981
    • (1981) Nonlinear Oscillations
    • Hagedorn, P.1
  • 5
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He, J.H. Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals, 26: 695-700(2005)
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 7
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for non-linear problems
    • He, J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-linear Mechanics 35: 37-43(2000)
    • (2000) International Journal of Non-linear Mechanics , vol.35 , pp. 37-43
    • He, J.H.1
  • 8
  • 9
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He, J.H. Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons & Fractals, 26: 695-700(2005)
    • (2005) Chaos Solitons & Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 11
    • 4344696077 scopus 로고    scopus 로고
    • Asymptotology by homotopy perturbation method
    • He, J.H. Asymptotology by homotopy perturbation method, Applied Mathematics and Computation, 156: 591-596(2004)
    • (2004) Applied Mathematics and Computation , vol.156 , pp. 591-596
    • He, J.H.1
  • 12
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: A new nonlinear analytical technique
    • He, J.H. Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135: 73-79(2003)
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 73-79
    • He, J.H.1
  • 13
    • 34247154842 scopus 로고    scopus 로고
    • A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity
    • doi:10.1016/j.chaos.2006.04.013
    • Öziş, T., Yildirim, A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos Solitons & Fractals, doi:10.1016/j.chaos.2006.04.013
    • Chaos Solitons & Fractals
    • Öziş, T.1    Yildirim, A.2
  • 14
    • 34249869084 scopus 로고    scopus 로고
    • A Coupled Method of He's Homotopy Perturbation Method and Modified Lindstedt-Poincaré Method for Traveling Wave Solutions of the Nonlinear Klein-Gordon Equation
    • submitted
    • Öziş, T. Yildirim, A. A Coupled Method of He's Homotopy Perturbation Method and Modified Lindstedt-Poincaré Method for Traveling Wave Solutions of the Nonlinear Klein-Gordon Equation, J. of Franklin Institute (2007) (submitted)
    • (2007) J. of Franklin Institute
    • Öziş, T.1    Yildirim, A.2
  • 15
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • He, J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151 (1): 287-292(2004)
    • (2004) Applied Mathematics and Computation , vol.151 , Issue.1 , pp. 287-292
    • He, J.H.1
  • 16
    • 85039210760 scopus 로고    scopus 로고
    • He, J.H. Non-Perturbative Methods for Strongly nonlinear Problems, dissertation.deverlag im Internet GmbH, Berlin, 2006
    • He, J.H. Non-Perturbative Methods for Strongly nonlinear Problems, dissertation.deverlag im Internet GmbH, Berlin, 2006
  • 17
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.H. Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20: 1141-1199(2006)
    • (2006) International Journal of Modern Physics B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 18
    • 33746584753 scopus 로고    scopus 로고
    • New interpretation of homotopy perturbation method
    • He, J.H. New interpretation of homotopy perturbation method, International Journal of Modern Physics B 20: 2561-2568(2006)
    • (2006) International Journal of Modern Physics B , vol.20 , pp. 2561-2568
    • He, J.H.1
  • 19
    • 18844391045 scopus 로고    scopus 로고
    • Limit cycle and bifurcation of nonlinear problems
    • He, J.H. Limit cycle and bifurcation of nonlinear problems, Chaos Solitons & Fractals, 26 (3): 827-833(2005)
    • (2005) Chaos Solitons & Fractals , vol.26 , Issue.3 , pp. 827-833
    • He, J.H.1
  • 20
    • 4243080805 scopus 로고    scopus 로고
    • Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method
    • Liu, H.M. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method, Chaos, Solitons & Fractals, 23(2): 577-579(2005)
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.2 , pp. 577-579
    • Liu, H.M.1
  • 21
    • 4444377082 scopus 로고    scopus 로고
    • Determination of limit cycles for strongly nonlinear oscillators
    • Art. No. 1743012003
    • He, J.H. Determination of limit cycles for strongly nonlinear oscillators, Physical Review Letters, 90 (17): Art. No. 174301(2003)
    • Physical Review Letters , vol.90 , Issue.17
    • He, J.H.1
  • 22
    • 33749550434 scopus 로고    scopus 로고
    • Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators
    • Öziş,T., Yildirim, A. Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators, Chaos Solitons & Fractals ,32 (2007) 445-448
    • (2007) Chaos Solitons & Fractals , vol.32 , pp. 445-448
    • Öziş, T.1    Yildirim, A.2
  • 24
    • 85039210288 scopus 로고    scopus 로고
    • Determination of frequency-amplitude relation for Duffing-Harmonic Oscillator by the Energy Balance Method
    • accepted
    • Öziş, T., Yildirim, A. Determination of frequency-amplitude relation for Duffing-Harmonic Oscillator by the Energy Balance Method, Computers and Mathematics with applications (accepted)
    • Computers and Mathematics with applications
    • Öziş, T.1    Yildirim, A.2
  • 25
    • 33748424980 scopus 로고    scopus 로고
    • An analytical approximate technique for a class of strongly non-linear oscillators
    • doi:10.1016/j.ijnonlinmec.2006.01.006
    • Wu,B.S., Sun,W.P., Lim, C.W., An analytical approximate technique for a class of strongly non-linear oscillators, International Journal of Non-Linear Mechanics doi:10.1016/j.ijnonlinmec.2006.01.006
    • International Journal of Non-Linear Mechanics
    • Wu, B.S.1    Sun, W.P.2    Lim, C.W.3
  • 26
    • 0001308274 scopus 로고    scopus 로고
    • Analytical solution of a nonlinear oscillator by the linearized perturbation technique
    • He, J.H. Analytical solution of a nonlinear oscillator by the linearized perturbation technique, Communication in Nonlinear Science & Numerical Simulation, 4(2): 109-113(1999)
    • (1999) Communication in Nonlinear Science & Numerical Simulation , vol.4 , Issue.2 , pp. 109-113
    • He, J.H.1
  • 27
    • 0033313212 scopus 로고    scopus 로고
    • Modified straightforward expansion
    • He, JH. Modified straightforward expansion, Meccanica, 34 (4): 287-289(1999)
    • (1999) Meccanica , vol.34 , Issue.4 , pp. 287-289
    • He, J.H.1
  • 28
    • 0025887981 scopus 로고
    • A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
    • Cheung, Y. K., Mook, S.H., Lau,S.L. A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators, International Journal of Non-linear Mechanics,26: 367-378(1991)
    • (1991) International Journal of Non-linear Mechanics , vol.26 , pp. 367-378
    • Cheung, Y.K.1    Mook, S.H.2    Lau, S.L.3
  • 29
    • 0037058127 scopus 로고    scopus 로고
    • A modified Micken's procedure for certain non-linear oscillators
    • Lim,C.W., Wu, B.S. A modified Micken's procedure for certain non-linear oscillators, Journal of Sound and Vibration, 257(1) (2002) 202-206
    • (2002) Journal of Sound and Vibration , vol.257 , Issue.1 , pp. 202-206
    • Lim, C.W.1    Wu, B.S.2
  • 30
    • 29344467932 scopus 로고    scopus 로고
    • A modified eigen-function expansion approximation for nonlinear oscillating equations
    • Xiong, Z.G., Hu, H., Tang, Q. A modified eigen-function expansion approximation for nonlinear oscillating equations, Journal of Sound and Vibration, 290: 1315-1321 (2006)
    • (2006) Journal of Sound and Vibration , vol.290 , pp. 1315-1321
    • Xiong, Z.G.1    Hu, H.2    Tang, Q.3
  • 32
    • 0036489498 scopus 로고    scopus 로고
    • Modified Lindstedt-Poincaré methods for some strongly non-linear oscillations Part I: Expansion of a constant
    • He, J.H. Modified Lindstedt-Poincaré methods for some strongly non-linear oscillations Part I: expansion of a constant, International Journal of Non-linear Mechanics, 37: 309-314 (2002)
    • (2002) International Journal of Non-linear Mechanics , vol.37 , pp. 309-314
    • He, J.H.1
  • 34
    • 0037461472 scopus 로고    scopus 로고
    • Analysis of non-linear oscillators having non-polynomial elastic terms
    • Mickens, R. E. Analysis of non-linear oscillators having non-polynomial elastic terms, Journal of Sound and Vibration 255(4): 789-792(2002)
    • (2002) Journal of Sound and Vibration , vol.255 , Issue.4 , pp. 789-792
    • Mickens, R.E.1
  • 35
    • 34250663068 scopus 로고    scopus 로고
    • He's parameter-expanding methods for strongly nonlinear oscillators
    • doi: 10.1016/j.cam.2006.07.020
    • Xu, L. He's parameter-expanding methods for strongly nonlinear oscillators, Journal of Computational and Applied Mathematics, (2006), doi: 10.1016/j.cam.2006.07.020
    • (2006) Journal of Computational and Applied Mathematics
    • Xu, L.1
  • 37
    • 0037468846 scopus 로고    scopus 로고
    • Frequencies of oscillators with fractional-power non-linearities
    • Gottlieb, H.P.W. Frequencies of oscillators with fractional-power non-linearities, Journal of Sound and vibration, 261: 557-566 (2003)
    • (2003) Journal of Sound and vibration , vol.261 , pp. 557-566
    • Gottlieb, H.P.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.