Volume 5 Number 4 (Oct. 2015)
Home > Archive > 2015 > Volume 5 Number 4 (Oct. 2015) >
IJAPM 2015 Vol.5(4): 259-266 ISSN: 2010-362X
doi: 10.17706/ijapm.2015.5.4.259-266

An Exponential Spline Approach to the Generalized Sine-Gordon Equation

Reza Mohammadi
Abstract—The nonlinear sine-Gordon equation is used to model many nonlinear phenomena. Numerical simulation of the solution to the one-dimensional generalized sine-Gordon equation is considered here. Two implicit three time-level difference schemes are developed, by using the exponential spline function approximation. We consider both Dirichlet and Neumann boundary conditions. The resulting spline difference schemes are analyzed for local truncation error, stability and convergence. It has been shown that by suitably choosing the parameters, we can obtain two schemes of O(k2+k2h2+h2) and O(k2+k2h2+h4). In the end, some numerical examples are provided to demonstrate the effectiveness of the proposed schemes.

Index Terms—Exponential spline, finite difference, generalizedsine-gordon equation, dirichlet and neumann boundary conditions, stability analysis, convergence.

The author is with the Department of Mathematics, University of Neyshabur, Postal code 91136-899 Neyshabur, Iran (email: rez.mohammadi@gmail.com).

Cite: Reza Mohammadi, "An Exponential Spline Approach to the Generalized Sine-Gordon Equation," International Journal of Applied Physics and Mathematics vol. 5, no. 4, pp. 259-266, 2015.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Nanowerk Database, Google Scholar and ProQuest
E-mail: ijapm@iap.org
  • Dec 26, 2017 News!

    IJAPM Vol 6, No 1-No 4 have been indexed by EI (Inspec)   [Click]

  • Dec 27, 2017 News!

    Vol 8, No 1 has been published with online version     [Click]

  • Dec 26, 2017 News!

    IJAPM Vol 5, No 4 has been indexed by EI (Inspec)     [Click]

  • Nov 15, 2017 News!

    The papers published in Vol 7, No 4 have all received dois from Crossref

  • Sep 28, 2017 News!

    Vol 7, No 4 has been published with online version     [Click]

  • Read more>>