Numerical solution of GRLW equation using Sinc-collocation method

Computer Physics Communications

Volumn 181, Issue 7, 2010, Pages 1266-1274

  Mokhtari, Reza ^a   Mohammadi, Maryam ^a  

^a ISFAHAN UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

MRLW equation; RLW equation; Sinc collocation method

Indexed keywords

BASIS FUNCTIONS; COLLOCATION METHOD; CONSERVATION PROPERTIES; GENERALIZED REGULARIZED LONG-WAVE EQUATIONS; MESHFREE TECHNIQUE; NUMERICAL SOLUTION; RLW EQUATION; SINC-COLLOCATION METHOD; SINGLE SOLITON; SOLITARY WAVE;

NUMERICAL ANALYSIS; SOLITONS;

EQUATIONS OF MOTION;

EID: 77953131119     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2010.03.015     Document Type: Article

References (45)

1. Peregrine D.H. Calculations of the development of an undular bore. J. Fluid Mech. 25 (1966) 321-330
2. Peregrine D.H. Long waves on a beach. J. Fluid Mech. 27 (1967) 815-827
3. Zhang L. A finite difference scheme for generalized regularized long-wave equation. Appl. Math. Comput. 168 (2005) 962-972
4. Durán A., and López-Marcos M.A. Numerical behaviour of stable and unstable solitary waves. Appl. Numer. Math. 42 (2002) 95-116
5. Bona J.L., McKinney W.R., and Restrepo J.M. Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation. J. Nonlinear Sci. 10 (2000) 603-638
6. Djidjeli K., Price W.G., Twizell E.H., and Cao Q. A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations. Comm. Numer. Methods Engrg. 19 (2003) 847-863
7. Xie S., Kim S., Woo G., and Yi S. A numerical method for the generalized regularized long wave equation using a reproducing kernel function. SIAM J. Sci. Comput. 30 (2008) 2263-2285
8. Benjamin T.B., Bona J.L., and Mahony J.J. Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R. Soc. Lond. Ser. A 272 (1972) 47-78
9. Daǧ I. Least-square quadratic B-spline finite element method for the regularized long wave equation. Comput. Methods Appl. Mech. Engrg. 182 (2000) 205-215
10. Daǧ I., and Özer M.N. Approximation of the RLW equation by the least square cubic B-spline finite element method. Appl. Math. Model. 25 (2001) 221-231
11. Gardner L.R.T., Gardner G.A., and Dogan A. A least-square finite element method for the RLW equation. Comm. Numer. Methods Engrg. 12 (1996) 795-804
12. Daǧ I., Dogan A., and Saka B. B-spline collocation methods for numerical solutions of the RLW equation. Int. J. Comput. Math. 80 (2003) 743-757
13. Esen A., and Kutluay S. Application of a lumped Galerkin method to the regularized long wave equation. Appl. Math. Comput. 174 (2006) 833-845
14. Daǧ I., Saka B., and Irk D. Galerkin method for the numerical solution of the RLW equation using quintic B-splines. J. Comput. Appl. Math. 190 (2006) 532-547
15. Raslan K.R. A computational method for the regularized long wave equation. Appl. Math. Comput. 167 (2005) 1101-1118
16. Saka B., Daǧ I., and Dogan A. Galerkin method for the numerical solution of the RLW equation using quadratic B-spline. Int. J. Comput. Math. 81 (2004) 727-739
17. Saka B., and Daǧ I. A Collocation method for the numerical solution of the RLW equation using cubic B-spline basis. Arab. J. Sci. Eng. 30 (2005) 39-50
18. Dogan A. Numerical solution of RLW equation using linear finite elements within Galerkin's method. Appl. Math. Model. 26 (2002) 771-783
19. Gardner L.R.T., Gardner G.A., and Daǧ I. A B-spline finite element method for the regularized long wave equation. Comm. Numer. Methods Engrg. 11 (1995) 59-68
20. Dogan A. Numerical solution of regularized long wave equation using Petrov-Galerkin method. Comm. Numer. Methods Engrg. 17 (2001) 485-494
21. Siraj-ul-Islam, Had S., and Ali A. A meshfree method for the numerical solution of the RLW equation. J. Comput. Appl. Math. 223 (2009) 997-1012
22. Gardner L.R.T., Gardner G.A., Ayoub F.A., and Amein N.K. Approximations of solitary waves of the MRLW equation by B-spline finite element. Arab. J. Sci. Eng. 22 (1997) 183-193
23. Khalifa A.K., Raslan K.R., and Alzubaidi H.M. A collocation method with cubic B-splines for solving the MRLW equation. Comput. Appl. Math. 212 (2008) 406-418
24. Khalifa A.K., Raslan K.R., and Alzubaidi H.M. A finite difference scheme for the MRLW and solitary wave interactions. Appl. Math. Comput. 189 (2007) 346-354
25. Raslan K.R. Numerical study of the Modified Regularized Long Wave (MRLW) equation. Chaos Solitons Fractals 42 (2009) 1845-1853
26. Bellman R., Kashef B., and Casti J. Differential quadrature: Solution of nonlinear partial differential equations. J. Comput. Phys. 10 (1972) 40-52
27. Bert C., and Malik M. Differential quadrature method in computational mechanics. Appl. Mech. Rev. 49 (1996) 1-27
28. Dehghan M., and Mohebbi A. The combination of collocation, finite difference, and multigrid methods for solution of the two-dimensional wave equation. Numer. Methods Partial Differential Equations 24 (2008) 897-910
29. Dehghan M., and Mohebbi A. High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation. Numer. Methods Partial Differential Equations 25 (2009) 232-243
30. Dehghan M. Implicit collocation technique for heat equation with non-classic initial condition. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 461-466
31. Stenger F. A Sinc Galerkin method of solution of boundary value problems. Math. Comp. 33 (1979) 35-109
32. Wu X., Kong W., and Li C. Sinc collocation method with boundary treatment for two-point boundary value problems. J. Comput. Appl. Math. 196 (2006) 229-240
33. Dehghan M., and Saadatmandi A. The numerical solution of a nonlinear system of second-order boundary value problems using the sinc-collocation method. Math. Comput. Modelling 46 (2007) 1434-1441
34. Parand K., Dehghan M., and Pirkhedri A. Sinc-collocation method for solving the Blasius equation. Phys. Lett. A (2009) 10.1016/j.physleta.2009.09.005
35. Abdella K., Yu X., and Kucuk I. Application of the Sinc method to a dynamic elasto-plastic problem. J. Comput. Appl. Math. 223 (2009) 626-645
36. Stenger F. Summary of Sinc numerical methods. J. Comput. Appl. Math. 121 (2000) 379-420
37. Wu Y., and Wu X. Linearized and rational approximation method for solving non-linear Burger equation. Internat. J. Numer. Methods Fluids 45 (2004) 509-525
38. Revelli R., and Ridolfi L. Sinc collocation-interpolation method for the simulation of nonlinear waves. Comput. Math. Appl. 46 (2003) 1443-1453
39. Al-Khaled K. Sinc numerical solution for solitons and solitary waves. J. Comput. Appl. Math. 130 (2001) 283-292
40. Lund J., and Bowers K.L. Sinc Methods for Quadrature and Differential Equations (1992), SIAM, Philadelphia, PA
41. Stenger F. Numerical Methods Based on Sinc and Analytic Functions (1993), Springer, New York
42. Paley R.E.A.C., and Wiener N. Fourier Transforms in the Complex Domain. Colloquium Publication vol. XIX (1964), American Mathematical Society
43. Li Y., and Bona J.L. Analyticity of solitary-wave solutions of model equations for long waves. SIAM J. Math. Anal. 27 3 (1996) 725-737
44. Lienau C. Analytic representation theory of (R, +). J. Funct. Anal. 257 (2009) 3293-3308
45. Olver P.J. Euler operators and conservation laws of the BBM equation. Math. Proc. Cambridge Philos. Soc. 85 (1979) 143-159