A new numerical application of the generalized Rosenau-RLW equation

References:

1. Pan, X. and Zhang, L. Numerical simulation for general Rosenau-RLWequation: An average linearized conservative scheme", Mathematical Problems in Engineering, 2012, Article ID 517818, 15 pages (2012).
2. Pan, X., Zheng, K., and Zhang, L. Finite di_erence discretization of the Rosenau-RLW equation", Appl. Anal., 92, pp. 2578{2589 (2013).
3. Atouani, N. and Omrani, K. Galerkin _nite element method for the Rosenau-RLW equation", Computers and Mathematics with Applications, 66, pp. 289{303 (2013).
4. Yagmurlu, N.M., Karaagac, B., and Kutluay, S. Numerical solutions of rosenau-RLW equation using Galerkin cubic B-spline _nite element method", American Journal of Computational and Applied Mathematics, 7, pp. 1{10 (2017).
5. Wongsaijai, B. and Poochinapan, K. A three-level average implicit finite difference scheme to solve equation obtained by coupling the Rosenau-KdV equation and the Rosenau-RLW equation", Applied Mathematics and Computation, 245, pp. 289{304 (2014).
6. Zuo, J., Zhang, Y.M., Zhang, T.D., et al. A new conservative difference scheme for the general Rosenau- RLW equation", Bound. Value Probl., 2010, pp. 1{13 (2010).
7. Pan, X. and Zhang, L. Numerical simulation for general Rosenau-RLWequation: An average linearized conservative scheme", Mathematical Problems in Engineering, 2012, Article ID 517818, 15 pages (2012). 8. Mittal, R.C. and Jain, R.K. Numerical solution of general Rosenau-RLW, equations using quintic Bsplines collocation method", Commun. Numer. Anal., Article ID cna-00129, pp. 1{16 (2012). 9. Wongsaijai, B., Poochinapan, K., and Disyadej, T. A compact _nite di_erence method for solving the general Rosenau-RLW equation", IAENG International Journal of Applied Mathematics, 44, pp. 1{8 (2014). 10. Wang, H., Wang, J., and Li, S. A new conservative nonlinear high order compact _nite di_erence scheme for the general Rosenau-RLWequation", Bound. Value Probl., 2015, pp. 1{16 (2015). 11. Wang, H., Li, S., and Wang, J. "A conservative weighted _nite di_erence scheme for the general Rosenau-RLW equation", Comp. Appl. Math., 36, pp. 63{78 (2017). 12. Ar_, M. and Dereli, Y. Numerical solutions of the general Rosenau-RLW equation using meshless kernel based method of lines", Journal of Physics: Conference Series, 766, pp. 1{6 (2016). 13. Cai, W., Sun, Y., and Wang, Y. Variational discretizations for the generalized Rosenau type equations", Appl. Math.Comput., 271, pp. 860{873 (2015). 14. Korteweg, D.J. and de Vries, G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave", Philosophical Magazine, 39, pp. 422{443 (1895). 15. Raslan, K.R., El-Danaf, Talaat S., and Ali, Khalid K. Application of linear combination between cubic B-spline collocation methods with di_erent basis for solving the KdV equation", Computational Methods for Di_erential Equations, 4, pp. 191{204 (2016). 16. Raslan, K.R., El-Danaf, Talaat S., and Ali, Khalid K. Collocation method with quintic b-spline method for solving hirota-satsuma coupled KDV equation", International Journal of Applied Mathematical Research, 5, pp. 123{131 (2016). 17. Raslan, K.R., El-Danaf, Talaat, S., and Ali, Khalid, K. New numerical treatment for solving the KDV equation", Journal of Abstract and Computational Mathematics, 2, pp. 1{12 (2017). 18. Peregrine, D.H. Calculations of the development of an undular bore", J. Fluid Mech., 25, pp. 321{330 (1966). 19. El-Danaf, Talaat S., Raslan, K.R., and Ali, Khalid K. New numerical treatment for the generalized regularized long wave equation based on _nite di_erence scheme", Int. J. of S. Comp. and Eng. (IJSCE)', 4, pp. 16{24 (2014). 20. El-Danaf, Talaat, S., Raslan, K.R., and Ali, Khalid K. Collocation method with cubic B-splines for solving the GRLWequation", Int. J. of Num. Meth. and Appl., 15, pp. 39{59 (2016). 21. Raslan, K.R., El-Danaf, Talaat S., and Ali, Khalid K. New exact solution of coupled generalized regularized long wave equation", Journal of the Egyptian Mathematical Society, 25, pp. 400{405 (2017). 22. Raslan, K.R., Ali, Khalid K., and Shallal, Muhannad A. Solving the space-time fractional RLWand MRLW equations using modi_ed extended tanh method with the Riccati equation", British Journal of Mathematics & Computer Science, 21, pp. 1{15 (2017). 23. El-Danaf, Talaat S., Raslan, K.R., and Ali, Khalid K. Non-polynomial spline method for solving the generalized regularized long wave equation", Communication in Mathematical Modeling and Applications, 2, pp. 1{17 (2017). 24. Karakoc, S.B.G., Ucar, Y., and Yagmurlu, N.M. Numerical solutions of the MRLW equation by cubic Bspline galerkin _nite element method", Kuwait Journal of Science, 42, pp. 141{159, (2015). S.B.G. Karakoc/Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 772{783 783 25. Rouzegar, J. and Sharifpoor, R. Abdoli. A _nite element formulation for bending analysis of isotropic and orthotropic plates based on two-variable re_ned plate theory", Scientia Iranica, B, 22, pp. 196{207 (2015). 26. Pan, X. and Zhang, L. A new _nite di_erence scheme for the Rosenau-Burgers equation", Applied Mathematics and Computation, 218, pp. 8917{8924 (2012). 27. Rosenau, P. A quasi-continuous description of a nonlinear transmission line", Phys. Scripta., 34, pp. 827{829 (1986). 28. Rosenau, P. Dynamics of dense discrete systems", Progr. Theory. Phys., 79, pp. 1028{1042 (1988). 29. Park, M.A. On the Rosenau equation", Math. Appl. Comput., 9, pp. 145{152 (1990). 30. Karakoc, S.B.G. and Zeybek, H. Solitary-wave solutions of the GRLW equation using septic B-spline collocation method", Applied Mathematics and Computation, 289, pp. 159{171 (2016). 31. Prenter, P.M., Splines and Variational Methods, John Wiley & Sons, New York, NY, USA (1975). 32. Esen, A. A lumped Galerkin method for the numerical solution of the modi_ed equal-width wave equation using quadratic B-splines", International Journal of Computer Mathematics, 83, pp. 449{459 (2006). 33. Saka, B., S_ahin, A., and Da_g, I. B-spline collocation algorithms for numerical solution of the RLW equation", Numer. Methods Partial Di_erential Eq., 27, pp. 581{607 (2011). 34. Geyikli, T. and Karakoc, S.B.G. Septic B-spline collocation method for the numerical solution of the modi_ed equal width wave equation", Applied Mathematics, 2, pp. 739{749 (2011). 35. Ak, T., Dhawan, S., Karakoc, S.B.G., et al. Numerical study of Rosenau-KdV equation using _nite element method based on collocation approach", Mathematical Modelling and Analysis, 22, pp. 373{383 (2017). 36. Karakoc, S.B.G., Yagmurlu, N.M., and Ucar, Y. A numerical approximation to solution of the modi_ed regularized long wave (MRLW) equation using quintic B-splines", Bound. Value Probl., 27, pp. 1{17 (2013). 37. Ak, T., Karakoc, S.B.G., and Biswas, A. Application of Petrov-Galerkin _nite element method to shallow water waves model: Modi_ed Korteweg-de Vries equation", Scientia Iranica B., 24, pp. 1148{1159 (2017). 38. Hassan, H.N. An accurate numerical solution for the modi_ed equal width wave equation using the Fourier pseudo-spectral method", Journal of Applied Mathematics and Physics, 4, pp. 1054{1067 (2016). 39. Essa, Y.M. Abo Multigrid method for the numerical solution of the modi_ed equal width wave equation", Applied Mathematics, 7, pp. 1140{1147 (2016). 40. Karakoc, S.B.G. and Geyikli, T. Numerical solution of the modi_ed equal width wave equation", International Journal of Di_erential Equations, 2012, pp. 1{ 15 (2012).