Numerical solution of complex modified Korteweg-de Vries equation by Petrov-Galerkin method

Applied Mathematics and Computation

Volumn 202, Issue 2, 2008, Pages 520-531

  Ismail, M S ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

CMKdV equation; Cubic B splines; Petrov Galerkin method; Solitons interaction

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; GALERKIN METHODS; LINEAR EQUATIONS; NEWTON-RAPHSON METHOD; NUMERICAL ANALYSIS; SPLINES;

B-SPLINES; CONSERVED QUANTITIES; CUBIC B-SPLINES; ELSEVIER (CO); FOURTH ORDER ACCURACY; IMPLICIT MIDPOINT RULE; KORTEWEG-DE VRIES (MKDV) EQUATION; NEUMANN METHOD; NEWTON'S METHODS; NON-LINEAR; NUMERICAL SCHEMES; NUMERICAL SOLUTIONS; PETROV-GALERKIN (PG) METHODS; SECOND ORDERS; SOLITARY WAVES; SOLITON SOLUTIONS; TEST FUNCTIONS; TRIAL FUNCTIONS; UNCONDITIONALLY STABLE (US);

NUMERICAL METHODS;

EID: 48049119494     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.02.033     Document Type: Article

References (18)

1. Christie I., Griffiths D., Mitchell A., and Sanz-Serna J.M. Product approximation for non-linear problems in the finite element method. IMA J. Numer. Anal. 1 (1981) 253-266
2. Debenath L. Nonlinear Partial Differential Equations (1997), Birkhäuser, Boston
3. Halim A.A., Kshevetskii S.P., and Leble S.B. Numerical integration of a coupled Korteweg-de Vries System. Comput. Math. Appl. 45 (2003) 581-591
4. Halim A.A., and Leble S.B. Analytical and numerical solution of coupled KdV-MKdV system. Chaos Soliton Fract. 19 (2004) 99-108
5. Hirota R., and Satsuma J. Soliton solution of the coupled KdV system. Phys. Lett. A 85 (1981) 407-409
6. M.S. Ismail, Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method, Math. Comput. Simul., in press.
7. Ismail M.S., and Taha T.R. A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation. Math. Comput. Simul. 74 (2007) 302-311
8. Ismail M.S., and Alamri S.Z. Highly accurate finite difference method for coupled nonlinear Schrödinger equation. Int. J. Comput. Math. 81 3 (2004) 333-351
9. Ismail M.S., and Taha T.R. Numerical simulation of coupled nonlinear Schrödinger equation. Math. Comput. Simul. 56 (2001) 547-562
10. Mashat D.S., Wazzan L.A., and Ismail M.S. Petrov-Galerkin method and K(2, 2). Int. J. Comput. Math. 83 3 (2006) 331-343
11. Muslu G.M., and Erabay H.A. A split-step fourier method for the complex modified Korteweg-de Vries equation. Comput. Math. Appl. 45 (2003) 503-514
12. Sanz-Serna J.M., and Christie I. Petrov-Galerkin methods for nonlinear dispersive waves. J. Comput. Phys. 39 (1981) 94-103
13. Taha T.R., and Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrö dinger equation. J. Comput. Phys. 55 (1984) 203-230
14. Taha T.R., and Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations. IV. Numerical, Korteweg-de Vries equation. J. Comput. Phys. 55 (1984) 231-253
15. Taha T.R., and Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations. IV. Numerical, modified Korteweg-de Vries equation. J. Comput. Phys. 77 (1988) 540-548
16. Taha T.R. Numerical simulations of the complex modified Korteweg-de Vries equation. Math. Comput. Simul. 37 (1994) 461-467
17. Wazwaz A.M. The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations. Comput. Math. Appl. 49 (2005) 1101-1112
18. Zhu S. A difference scheme for the coupled KdV equation. Commun. Nonlinear Sci. Numer. Simul. 4 1 (1999) 60-63