Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 343497, 8 pages
http://dx.doi.org/10.1155/2014/343497
Research Article

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand 247667, India

Received 11 May 2014; Accepted 16 July 2014; Published 10 August 2014

Academic Editor: Nikolai A. Kudryashov

Copyright © 2014 R. C. Mittal and Rachna Bhatia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. K. Perring and T. H. R. Skyrme, “A model unified field equation,” Nuclear Physics, vol. 31, pp. 550–555, 1962. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. A. Barone, F. Esposito, C. J. Magee, and A. C. Scott, “Theory and applications of the sine-Gordon equation,” La Rivista del Nuovo Cimento, vol. 1, no. 2, pp. 227–267, 1971. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Dehghan and A. Shokri, “Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions,” Journal of Computational and Applied Mathematics, vol. 230, no. 2, pp. 400–410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. G. Ben-Yu, P. J. Pascual, M. J. Rodriguez, and L. Vázquez, “Numerical solution of the sine-Gordon equation,” Applied Mathematics and Computation, vol. 18, no. 1, pp. 1–14, 1986. View at Publisher · View at Google Scholar · View at Scopus
  5. A. G. Bratsos and E. H. Twizell, “The solution of the sine-Gordon equation using the method of lines,” International Journal of Computer Mathematics, vol. 61, no. 3-4, pp. 271–292, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. A. Mohebbi and M. Dehghan, “High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 537–549, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. X. Kuang and L. H. Lu, “Two classes of finite-difference methods for generalized sine-Gordon equations,” Journal of Computational and Applied Mathematics, vol. 31, no. 3, pp. 389–396, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. G. Bratsos and E. H. Twizell, “A family of parametric finite-difference methods for the solution of the sine-Gordon equation,” Applied Mathematics and Computation, vol. 93, no. 2-3, pp. 117–137, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. W. Wei, “Discrete singular convolution for the sine-Gordon equation,” Physica D, vol. 137, no. 3-4, pp. 247–259, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. B. Batiha, M. S. M. Noorani, and I. Hashim, “Numerical solution of sine-Gordon equation by variational iteration method,” Physics Letters A, vol. 370, no. 5-6, pp. 437–440, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. C. Zheng, “Numerical solution to the sine-Gordon equation defined on the whole real axis,” SIAM Journal on Scientific Computing, vol. 29, no. 6, pp. 2494–2506, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. G. Bratsos, “A fourth order numerical scheme for the one-dimensional sine-Gordon equation,” International Journal of Computer Mathematics, vol. 85, no. 7, pp. 1083–1095, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. M. Dehghan and A. Shokri, “A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions,” Numerical Methods for Partial Differential Equations, vol. 24, no. 2, pp. 687–698, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. Dehghan and D. Mirzaei, “The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation,” Numerical Methods for Partial Differential Equations, vol. 24, no. 6, pp. 1405–1415, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J. Rashidinia and R. Mohammadi, “Tension spline solution of nonlinear sine-Gordon equation,” Numerical Algorithms, vol. 56, no. 1, pp. 129–142, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Li-Min and W. Zong-Min, “A numerical method for one-dimensional nonlinear sine-Gordon equation using multiquadric quasi-interpolation,” Chinese Physics B, vol. 18, no. 8, pp. 3099–3103, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. Z.-W. Jiang and R.-H. Wang, “Numerical solution of one-dimensional Sine-Gordon equation using high accuracy multiquadric quasi-interpolation,” Applied Mathematics and Computation, vol. 218, no. 15, pp. 7711–7716, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. Kaya, “A numerical solution of the sine-Gordon equation using the modified decomposition method,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 309–317, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. M. Uddin, S. Haq, and G. Qasim, “A meshfree approach for the numerical solution of nonlinear sine-Gordon equation,” International Mathematical Forum, vol. 7, no. 21–24, pp. 1179–1186, 2012. View at Google Scholar · View at MathSciNet
  20. S. Gottlieb, C.-W. Shu, and E. Tadmor, “Strong stability-preserving high-order time discretization methods,” SIAM Review, vol. 43, no. 1, pp. 89–112 (electronic), 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. R. C. Mittal and R. Bhatia, “Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method,” Applied Mathematics and Computation, vol. 220, pp. 496–506, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus