A comparative study of numerical solutions of a class of KdV equation

Applied Mathematics and Computation

Volumn 199, Issue 2, 2008, Pages 425-434

  Khattak, A J ^a   Siraj ul Islam, ^b  

^a GIK INSTITUTE OF ENGINEERING SCIENCES AND TECHNOLOGY   (Pakistan)

^b UNIVERSITY OF ENGINEERING AND TECHNOLOGY   (Pakistan)

Author keywords

Collocation method; Gaussian; Korteweg de Vries equation; Multiquadric; Radial basis functions; Solitons

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FUNCTION EVALUATION; GAUSSIAN DISTRIBUTION; PROBLEM SOLVING;

COLLOCATION METHOD; KORTEWEG-DE VRIES EQUATION; RADIAL BASIS FUNCTIONS;

POLYNOMIALS;

EID: 42949092656     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.10.002     Document Type: Article

References (17)

1. 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. Philos. Mag. 39 (1895) 422-443
2. Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Korteweg-de Vries equation and generalizations, VI, methods for exact solution. Comm. Pure Appl. Math. 27 (1974) 97-133
3. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 (1971) 1192-1194
4. Hirota R. Exact envelope-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14 (1973) 805-809
5. Zabuskay N.J. A synergetic approach to problem of nonlinear dispersive wave propagation and interaction. In: Ames W. (Ed). Proceedings of the Symposium on Nonlinear Partial Differential Equations (1967), Academic Press 223-258
6. Fornberg B., and Whitham G.B. A numerical and theoretical study of certain nonlinear wave phenomena. Philos. Trans. Roy. Soc. 289 (1978) 373-404
7. Kansa II E.J. Multiquadric - a scattered data approximation scheme with applications to computational fluid dynamics. Comput. Math. Appl. 19 (1990) 147-161
8. Zabuskay N.J., and Kuruskal M.D. Interaction of solitons in a collisionless plasma and recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-243
9. Goda K. On instability of some finite difference schemes for Korteweg-de Vries equation. J. Phys. Soc. Jpn. 39 (1975) 229-236
10. Vliengenthart A.C. On finite difference methods for the Korteweg-de Vries equation. J. Eng. Math. 5 (1971) 137-155
11. Gardner G.A., Ali A.H.A., and Gardner L.R.T. A finite element solution for the Korteweg-de Vries equation using cubic B-spline shape functions. In: Gruber R., Periaux J., and Shaw R.P. (Eds). ISNME-89 vol. 2 (1989), Springer, Berlin 565-570
12. G.A. Gardner, A. Ali, A numerical solutions for the Korteweg-de Vries equation using Galerkins method with Hermite polynomial shape functions, in: Proceedings of the International Conference on Modeling and Simulations, vol. 1C, Istanbul, 1988, pp. 81-93.
13. 2 in multiquadric interpolation. Comput. Math. Appl. 21 (1991) 29-42
14. Debnath L. Nonlinear Partial Differential Equations for Scientists and Engineers. second ed. (2005), Birkhäuser
15. Bhatta D.D., and Bhatti M.I. Numerical solution of KdV equation using modified Bernstein polynomials. Appl. Math. Comput. 174 (2006) 1255-1268
16. Taha T.R., and Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation. J. Comput. Phys. 55 (1984) 231-253
17. N Aksan E., and Özdes A. Numerical solution of Korteweg-de Vries equation by Galerkin B-Spline finite element method. Appl. Math. Comput. 175 (2006) 1256-1265