Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2017, Article ID 4796070, 9 pages
https://doi.org/10.1155/2017/4796070
Research Article

An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

1Mathematics Department, Science Faculty, Hacettepe University, Beytepe, 06800 Ankara, Turkey
2Mathematics Department, Atilim University, Incek, 06830 Ankara, Turkey

Correspondence should be addressed to Canan Koroglu; rt.ude.epettecah@ulgorokc

Received 25 July 2017; Accepted 9 October 2017; Published 1 November 2017

Academic Editor: Ming Mei

Copyright © 2017 Canan Koroglu and Ayhan Aydin. 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. A. Bekir, “On traveling wave solutions to combined KDV-mKDV Equation and modified Burgers-KDV Equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1038–1042, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. G. L. Lamb Jr., Elements of Soliton Theory, John Wiley & Sons, Inc, New York, NY, USA, 1980. View at MathSciNet
  3. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Consultants Bureau, New York, NY, USA, 1980.
  4. P. M. Manning and G. F. Margrave, “Introduction to non-standard finite-difference modelling,” CREWES Research Report 18, 2006. View at Google Scholar
  5. R. P. Agarwal, “Difference Equations and Inequalities: Theory, Methods, and Applications,” in Chapman & Hall/CRC, Pure and Applied Mathematics, vol. 228, CRC Press, New York, NY, USA, 2nd edition, 2000. View at Google Scholar · View at MathSciNet
  6. C. Liao and X. Ding, “Nonstandard finite difference variational integrators for multisymplectic PDEs,” Journal of Applied Mathematics, vol. 2012, Article ID 705179, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. L. W. Roeger, “Exact finite-difference schemes for two-dimensional linear systems with constant coefficients,” Journal of Computational and Applied Mathematics, vol. 219, no. 1, pp. 102–109, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. A. Aderogba, M. Chapwanya, J. Djoko Kamdem, and J. M. Lubuma, “Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schr\"odinger equation,” International Journal of Computer Mathematics, vol. 93, no. 11, pp. 1833–1844, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. B. Karasözen, “Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form,” International Journal of Computer Mathematics, vol. 66, no. 1-2, pp. 113–122, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  10. L. Zhang, L. Wang, and X. Ding, “Exact finite-difference scheme and nonstandard finite-difference scheme for coupled Burgers equation,” Advances in Difference Equations, 2014:122, 24 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. E. Mickens, Nonstandard finite difference models of differential equations, World Scientific, 1994. View at MathSciNet
  12. R. E. Mickens, Advances in the Applications of Nonstandard Finite Difference Schemes, R. E. Mickens, Ed., Wiley-Interscience, Singapore, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  13. L. Zhang, L. Wang, and X. Ding, “Exact finite difference scheme and nonstandard finite difference scheme for Burgers and Burgers-Fisher equations,” Journal of Applied Mathematics, Article ID 597926, Art. ID 597926, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. P. D. Lax and R. D. Richtmyer, “Survey of the stability of linear finite difference equations,” Communications on Pure and Applied Mathematics, vol. 9, pp. 267–293, 1956. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus