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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

Online
ISSN
1865-7109
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Volume 72, Issue 6

Issues

Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations

M.M. Fatih Karahan
Published Online: 2017-05-08 | DOI: https://doi.org/10.1515/zna-2016-0502

Abstract

A new perturbation method, multiple scales Lindstedt–Poincare (MSLP) is applied to jerk equations with cubic nonlinearities. Three different jerk equations are investigated. Approximate analytical solutions and periods are obtained using MSLP method. Both approximate analytical solutions and periods are contrasted with numerical and exact results. For the case of strong nonlinearities, obtained results are in good agreement with numerical and exact ones.

Keywords: Approximate Analytical Solutions; Multiple Scales Lindstedt–Poincare (MSLP) Method; Nonlinear Third-Order Ordinary Differential Equations; Perturbation Methods; Strongly Nonlinear Systems

References

  • [1]

    A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, John Wiley and Sons, New York 1979.Google Scholar

  • [2]

    A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley and Sons, New York 1981.Google Scholar

  • [3]

    R. E. Mickens, Oscillations in Planar Dynamic Systems, Word Scientific, Singapore 1996.Google Scholar

  • [4]

    Y. K. Cheung, S. H. Chen, and S. L. Lau, Int. J. Nonlinear Mech. 26, 367 (1991).Google Scholar

  • [5]

    Y. Y. Chen, L. W. Yan, R. K. L. Su, and B. Liu, J. Vib. Control. (2015). DOI: https://doi.org/10.1177/1077546315573915.Crossref

  • [6]

    Z. Li and J. Tang, Nonlinear Dyn. 84, 1201 (2016)Google Scholar

  • [7]

    Y. Y. Chen, S. H. Chen, and W. Zhao, Commun. Nonlinear Sci. Numer. Simulat. 48, 123 (2017).Google Scholar

  • [8]

    M. Pakdemirli, M. M. F. Karahan, and H. Boyacı, Math. Comput. Appl. 14, 31 (2009).Google Scholar

  • [9]

    M. Pakdemirli and M. M. F. Karahan, Math. Methods Appl. Sci. 33, 704 (2010).Google Scholar

  • [10]

    M. Pakdemirli, M. M. F. Karahan, and H. Boyacı, Math. Comput. Appl. 16, 879 (2011).Google Scholar

  • [11]

    M. Pakdemirli, Z. Naturforsch. 70, 829 (2015).Google Scholar

  • [12]

    M. Pakdemirli and G. Sari, Math. Comput. Appl. 20, 137 (2015).Google Scholar

  • [13]

    M. Pakdemirli and G. Sari, Comm. Num. Anal. 2015, 82 (2015).Google Scholar

  • [14]

    M. M. F. Karahan and M. Pakdemirli, Z. Naturforsch. 72, 59 (2017).Google Scholar

  • [15]

    H. Hu and Z. G. Xiong, J. Sound Vib. 278, 437 (2004).Google Scholar

  • [16]

    H. Hu, J. Sound Vib. 269, 409 (2004).Google Scholar

  • [17]

    H. P. W. Gottlieb, J. Sound Vib. 271, 671 (2004).Google Scholar

  • [18]

    B. S. Wu, C. W. Lim, and W. P. Sun, Phys. Lett. A. 354, 95 (2006).Google Scholar

  • [19]

    H. Hu, Phys. Lett. A. 372, 4205 (2008).Google Scholar

  • [20]

    H. Hu, M. Y. Zheng, and Y. J. Guo, Acta Mech. 209, 269 (2010).Google Scholar

  • [21]

    A. Y. T. Leung and Z. Guo, Int. J. Nonlinear Mech. 46, 898 (2011).Google Scholar

  • [22]

    X. Ma, L. Wei, and Z. Guo, J. Sound Vib. 314, 217 (2008).Google Scholar

  • [23]

    J. I. Ramos, Appl. Math. Comput. 215, 4304 (2010).Google Scholar

  • [24]

    J. I. Ramos, Nonlinear Anal. Real. 11, 1613 (2010).Google Scholar

  • [25]

    S-D. Feng and L-Q. Chen, Chinese J. Phys. 26, 124501-1 (2009).Google Scholar

About the article

Received: 2016-12-30

Accepted: 2017-04-06

Published Online: 2017-05-08

Published in Print: 2017-05-24


Citation Information: Zeitschrift für Naturforschung A, Volume 72, Issue 6, Pages 547–557, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2016-0502.

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