Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Nonlinear Engineering

Modeling and Application

Editor-in-Chief: Nakahie Jazar, Gholamreza

4 Issues per year


CiteScore 2017: 0.69

SCImago Journal Rank (SJR) 2017: 0.181
Source Normalized Impact per Paper (SNIP) 2017: 0.338

Online
ISSN
2192-8029
See all formats and pricing
More options …

An analytical method with Padé technique for solving of variational problems

H. Jaffarian / K. Sayevand / Sunil Kumar
  • Corresponding author
  • Department of Mathematics, National Institute of Technology Jamshedpur, 831014, Jharkhand, India
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-09-06 | DOI: https://doi.org/10.1515/nleng-2016-0065

Abstract

In this paper, the homotopy analysis method (HAM) is employed to solve a class of variational problems (VPs). By using the so-called ħ-curves, we determine the convergence parameter ħ, which plays key role to control convergence of solution series. Also we use Pade’ approximant to improve accuracy of the method. Two test example are given to clarify the applicability and efficiency of the proposed method.

Keywords: Variational problems; Euler-Lagrange; Homotopy analysis method; Padé

MSC 2010: 41A58; 39A10; 34K28; 41A10

References

  • [1]

    S. J. Liao: Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman Hall/ CRC Press, Boca Raton (2003).Google Scholar

  • [2]

    S. Abbasbandy, Y. Tan and S. J. Liao: Newton-homotopy analysis method for nonlinear equations, Appl. Math. Comput. 188(2007) 1794-1800.Web of ScienceGoogle Scholar

  • [3]

    S. Abbasbandy: Solitary wave solutions to the Kuramoto Sivashinsky equation by means of the homotopy analysis method, Nonlinear Dynam. 52 (2008) 35–40.CrossrefWeb of ScienceGoogle Scholar

  • [4]

    S. Abbasbandy and E.J. Parkes: Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method, Chaos Solitons Fract. 36 (2008) 581–591.CrossrefWeb of ScienceGoogle Scholar

  • [5]

    F. M. Allan: Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method, Chaos Solitons Fractals 39(2009) 1744-1752.CrossrefWeb of ScienceGoogle Scholar

  • [6]

    A. S. Bataineh, M. S. M. Nooraniand and I. Hashim: Solving systems of ODEs by homotopy analysis method, Commun. Nonlinear Sci. Numer. Simul. 13(2008) 2060-2070.CrossrefWeb of ScienceGoogle Scholar

  • [7]

    A. S. Bataineh, M. S. M. Noorani and I. Hashim: On a new reliable modifcation of homotopy analysis method, Commun. Nonlinear Sci. Numer. Simul. 14(2009) 409-423.CrossrefWeb of ScienceGoogle Scholar

  • [8]

    A. K. Alomari, M. S. M. Noorani and R. Nazar: Solution of delay differential equation by means of homotopy analysis method, Acta. Appl. Math. 108(2009) 395-412.Web of ScienceCrossrefGoogle Scholar

  • [9]

    Y. M. Chen and J. K. Liu: Improving convergence of incremental harmonic balance method using homotopy analysis method, Acta. Mech. Sin. 25(2009) 707-712.CrossrefWeb of ScienceGoogle Scholar

  • [10]

    S.J. Liao: The proposed homotopy analysis technique for the solution of nonlinear problems, PHD thesis, Shanghai Jiao Tong University (1992).Google Scholar

  • [11]

    S. J. Liao: An approximate solution technique not depending on small parameters: a special example, Int. J. Non-linear Mech. 30(1995) 371-380.CrossrefGoogle Scholar

  • [12]

    T. Odzijewicz, A. B. Malinowska and D. F. M. Torres: Fractional variational calculus with classical and combined Caputo derivatives, Nonlinear Anal . Theory Methods Appl. 75(3) (2012) 1507-1515.Web of ScienceCrossrefGoogle Scholar

  • [13]

    M. Ghasemi, M. Fardi and R. K. Ghaziani: Solution of system of the mixed Volterra-Fredholm integral equations by an analytical method, Math. Comput. Model. 58(2013) 1522-1530.CrossrefWeb of ScienceGoogle Scholar

  • [14]

    G. A. Baker: Essentials of Padé approximants, Academic Press, London (1975).Google Scholar

About the article

Received: 2016-10-11

Accepted: 2017-07-06

Published Online: 2017-09-06

Published in Print: 2017-12-20


Citation Information: Nonlinear Engineering, Volume 6, Issue 4, Pages 313–316, ISSN (Online) 2192-8029, ISSN (Print) 2192-8010, DOI: https://doi.org/10.1515/nleng-2016-0065.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in