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The Scientific World Journal
Volume 2014, Article ID 721865, 6 pages
http://dx.doi.org/10.1155/2014/721865
Research Article

Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method

Department of Mathematics, Politehnica University of Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania

Received 31 January 2014; Accepted 23 February 2014; Published 3 June 2014

Academic Editors: D. Baleanu, H. Jafari, and C. M. Khalique

Copyright © 2014 Constantin Bota and Bogdan Căruntu. 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.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. J. H. He and J.-H. He, “Recent development of the homotopy perturbation method,” Topological Methods in Nonlinear Analysis, vol. 31, no. 2, pp. 205–209, 2008. View at Google Scholar
  3. D. H. Peregrine, “Calculations of the development of an undular bore,” Journal of Fluid Mechanics, vol. 25, no. 2, pp. 321–330, 1966. View at Publisher · View at Google Scholar
  4. T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in non-linear dispersive systems,” Philosophical Transactions of the Royal Society A, vol. 272, pp. 47–48, 1972. View at Publisher · View at Google Scholar
  5. S. Kutluay and A. Esen, “A finite difference solution of the regularized long-wave equation,” Mathematical Problems in Engineering, vol. 2006, Article ID 85743, 14 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Hu, B. Hu, and Y. Xu, “C-N difference schemes for dissipative symmetric regularized long wave equations with damping term,” Mathematical Problems in Engineering, vol. 2011, Article ID 651642, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Pan and L. Zhang, “Numerical simulation for general Rosenau-RLW equation: an average linearized conservative scheme,” Mathematical Problems in Engineering, vol. 2012, Article ID 517818, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Hu and Y. Wang, “A high-accuracy linear conservative difference scheme for Rosenau-RLW equation,” Mathematical Problems in Engineering, vol. 2013, Article ID 870291, 8 pages, 2013. View at Publisher · View at Google Scholar
  9. Y. Liu, H. Li, Y. Du, and J. Wang, “Explicit multistep mixed finite element method for RLW equation,” Abstract and Applied Analysis, vol. 2013, Article ID 768976, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. H. O. Bakodah and M. A. Banaja, “The method of lines solution of the regularized long-wave equation using Runge-Kutta time discretization method,” Mathematical Problems in Engineering, vol. 2013, Article ID 804317, 8 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Pérez Pozo, R. Meneses, C. Spa, and O. Durán, “A meshless finite-point approximation for solving the RLW equation,” Mathematical Problems in Engineering, vol. 2012, Article ID 802414, 22 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. D. D. Ganji, H. Tari, and M. B. Jooybari, “Variational iteration method and homotopy perturbation method for nonlinear evolution equations,” Computers and Mathematics with Applications, vol. 54, no. 7-8, pp. 1018–1027, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Nawaz, S. Islam, I. A. Shah, M. Idrees, and H. Ullah, “Optimal homotopy asymptotic method to nonlinear damped generalized regularized long-wave equation,” Mathematical Problems in Engineering, vol. 2013, Article ID 503137, 13 pages, 2013. View at Publisher · View at Google Scholar
  14. H. Jafari, K. Sayevand, H. Tajadodi, and D. Baleanu, “Homotopy analysis method for solving Abel differential equation of fractional order,” Central European Journal of Physics, vol. 11, no. 10, pp. 1523–1527, 2013. View at Publisher · View at Google Scholar
  15. E. A.-B. Abde-Salam and E. A. Yousif, “Solution of nonlinear space-time fractional differential equations using the fractional Riccati expansion method,” Mathematical Problems in Engineering, vol. 2013, Article ID 846283, 6 pages, 2013. View at Publisher · View at Google Scholar