- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 587208, 15 pages
Numerical Solution of the Modified Equal Width Wave Equation
Department of Mathematics, Faculty of Education, İnönü University, 44280 Malatya, Turkey
Received 18 May 2011; Accepted 30 September 2011
Academic Editor: Sabri Arik
Copyright © 2012 Seydi Battal Gazi Karakoç and Turabi Geyikli. 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.
- L. R. T. Gardner and G. A. Gardner, “Solitary waves of the regularised long-wave equation,” Journal of Computational Physics, vol. 91, no. 2, pp. 441–459, 1990.
- L. R. T. Gardner and G. A. Gardner, “Solitary waves of the equal width wave equation,” Journal of Computational Physics, vol. 101, no. 1, pp. 218–223, 1992.
- P. J. Morrison, J. D. Meiss, and J. R. Cary, “Scattering of regularized-long-wave solitary waves,” Physica D. Nonlinear Phenomena, vol. 11, no. 3, pp. 324–336, 1984.
- Kh. O. Abdulloev, I. L. Bogolubsky, and V. G. Makhankov, “One more example of inelastic soliton interaction,” Physics Letters. A, vol. 56, no. 6, pp. 427–428, 1976.
- L. R. T. Gardner, G. A. Gardner, and T. Geyikli, “The boundary forced MKdV equation,” Journal of Computational Physics, vol. 113, no. 1, pp. 5–12, 1994.
- T. Geyikli and S. Battal Gazi Karakoç, “Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation,” Applied Mathematics, vol. 2, no. 6, pp. 739–749, 2011.
- T. Geyikli and S. Battal Gazi Karakoç, “Petrov-Galerkin method with cubic Bsplines for solving the MEW equation,” Bulletin of the Belgian Mathematical Society. In press.
- A. Esen, “A numerical solution of the equal width wave equation by a lumped Galerkin method,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 270–282, 2005.
- A. Esen, “A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines,” International Journal of Computer Mathematics, vol. 83, no. 5-6, pp. 449–459, 2006.
- B. Saka, “Algorithms for numerical solution of the modified equal width wave equation using collocation method,” Mathematical and Computer Modelling, vol. 45, no. 9-10, pp. 1096–1117, 2007.
- S. I. Zaki, “Solitary wave interactions for the modified equal width equation,” Computer Physics Communications, vol. 126, no. 3, pp. 219–231, 2000.
- S. I. Zaki, “Least-squares finite element scheme for the EW equation,” Computer Methods in Applied Mechanics and Engineering, vol. 189, no. 2, pp. 587–594, 2000.
- A.-M. Wazwaz, “The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants,” Communications in Nonlinear Science and Numerical Simulation, vol. 11, no. 2, pp. 148–160, 2006.
- B. Saka and Dağ, “Quartic B-spline collocation method to the numerical solutions of the Burgers' equation,” Chaos, Solitons and Fractals, vol. 32, no. 3, pp. 1125–1137, 2007.
- J. Lu, “He's variational iteration method for the modified equal width equation,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2102–2109, 2009.
- D. J. Evans and K. R. Raslan, “Solitary waves for the generalized equal width (GEW) equation,” International Journal of Computer Mathematics, vol. 82, no. 4, pp. 445–455, 2005.
- S. Hamdi, W. H. Enright, W. E. Schiesser, and J. J. Gottlieb, “Exact solutions of the generalized equal width wave equation,” in Proceedings of the International Conference on Computational Science and Its Application, vol. 2668, pp. 725–734, Springer, 2003.
- A. Esen and S. Kutluay, “Solitary wave solutions of the modified equal width wave equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1538–1546, 2008.
- P. M. Prenter, Splines and Variational Methods, John Wiley & Sons, New York, NY, USA, 1975.