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SECTION B

Non-polynomial splines method for numerical solutions of the regularized long wave equation

Pages 1591-1607 | Received 05 Jun 2013, Accepted 26 Jul 2014, Published online: 27 Aug 2014

References

  • T.B. Benjamin, J.L. Bona, and J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. R. Soc. Lond. Ser. A 272 (1972), pp. 47–78. doi: 10.1098/rsta.1972.0032
  • N.G. Chegini, A. Salaripanah, R. Mokhtari, and D. Isvand, Numerical solution of the regularized long wave equation using nonpolynomial splines, Nonlinear Dyn. 69 (2012), pp. 459–471. doi: 10.1007/s11071-011-0277-y
  • İ. Dağ and M. Naci Ozer, Approximation of the RLW equation by the least square cubic B-spline finite element method, Appl. Math. Model. 25 (2001), pp. 221–231. doi: 10.1016/S0307-904X(00)00030-5
  • İ. Dağ, B. Saka, and D. Irk, Application of cubic B-splines for numerical solution of the RLW equation, Appl. Math. Comput. 159 (2004), pp. 373–389. doi: 10.1016/j.amc.2003.10.020
  • İ. Dağ, B. Saka, and D. Irk, Galerkin method for the numerical solution of the RLW equation using quintic B-spline, J. Comput. Appl. Math. 190 (2006), pp. 532–547. doi: 10.1016/j.cam.2005.04.026
  • A. Dogan, Numerical solution of RLW equation using linear finite elements within Galerkin's method, Appl. Math. Model. 26 (2002), pp. 771–783. doi: 10.1016/S0307-904X(01)00084-1
  • A. Esen and S. Kutluay, Application of a lumped Galerkin method to the regularized long wave equation, Appl. Math. Comput. 174 (2006), pp. 833–845. doi: 10.1016/j.amc.2005.05.032
  • L.R.T. Gardner, G.A. Gardner, and A. Dogan, A least-squares finite element scheme for the RLW equation, Commun.Numer. Methods E. 12 (1996), pp. 795–804. doi: 10.1002/(SICI)1099-0887(199611)12:11<795::AID-CNM22>3.0.CO;2-O
  • İ. Dağ, Least-squares quadratic B-spline finite element method for the regularised long wave equation, Comput. Methods Appl. Mech. Eng. 182 ( 2000), pp. 205– 215. doi: 10.1016/S0045-7825(99)00106-1
  • S.U. Islam, S. Haq, and A. Ali, A meshfree method for the numerical solution of the RLW equation, J. Comput. Appl. Math. 223 (2009), pp. 997–1012. doi: 10.1016/j.cam.2008.03.039
  • A. Khan, I. Khan, T. Aziz, and M. Stojanovic, A variable-mesh approximation method for singularly perturbed boundary-value problems using cubic spline in tension, Int. J. Comput. Math. 81 (2004), pp. 1513–1518. doi: 10.1080/00207160412331284169
  • A. Korkmaz, Thesis of Master Degree, Eskisehir Osmangazi University, Eskisehir, Turkey, 2006 (Unpublished).
  • A. Korkmaz, Ph.D. dissertation, Eskisehir Osmangazi University, Eskisehir, Turkey, 2010 (Unpublished).
  • S. Kutluay and A. Esen, A finite difference solution of the regularized long-wave equation, Math. Probl. Eng. 2006 ( 2006), pp. 1–14. doi:10.1155/MPE/2006/85743.
  • M. Liquan and C. Yaping, Numerical solutions of RLW equation using Galerkin method with extrapolation techniques, Comput. Phys. Commun. 183(2012), pp. 1609–4655. doi: 10.1016/j.cpc.2012.02.029
  • R. Mokhtari and M. Mohammadi, Numerical solution of GRLW equation using Sinc-collocation method, Comput. Phys. Commun. 181 (2010), pp. 1266–1274. doi: 10.1016/j.cpc.2010.03.015
  • R. Mokhtari and S. Torabi Ziaratgahi, Numerical solution of RLW equation using integrated radial functions, Int. J. Appl. Comput. Math. 10 (2011), pp. 428–448.
  • D.H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech. 25(1996), pp. 321–330. doi: 10.1017/S0022112066001678
  • S. Pruess, Properties of splines in tension, J. Approx. Theory 17 (1976), pp. 86–96. doi: 10.1016/0021-9045(76)90113-1
  • K.R. Raslan, Solitary waves solutions of the MRLW equation using quintic B-splines, J. King Saud Univ – Sci. 22 (2010), pp. 161–166. doi: 10.1016/j.jksus.2010.04.004
  • B. Saka and İ Dağ, A Collocation method for the numerical solution of the RLW equation using cubic B-spline basis, Arab. J. Sci. Eng. 30 (2005), pp. 39–50.
  • B. Saka, İ. Dağ and A. Dogan, Galerkin method for the numerical solution of the RLW equation using quadratic B-spline, Int. J. Comput. Math. 81 (2004), pp. 727–739. doi: 10.1080/00207160310001650043
  • D. Schultz and R. Varga, An interpolation curve using a spline in tension, J. Math. Phys. 45 (1966), pp. 312–317.

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