A small time solutions for the Korteweg-de Vries equation

Applied Mathematics and Computation

Volumn 107, Issue 2-3, 2000, Pages 203-210

  Kutluay, S ^a   Bahadir, A R ^a   Ozdes A ^a  

^a INONU UNIVERSITY   (Turkey)

Author keywords

Heat balance integral; Korteweg de Vries equation; Soliton

Indexed keywords

EID: 0345849866     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10119-4     Document Type: Article

References (21)

1. R.M. Miura, Korteweg-de Vries equation and generalisations I. A remarkable explicit nonlinear transformation, Int. J. Math. Phys. 9 (1968) 1202-1204.
2. B. Fornberg, G.B. Whitham, A numerical and theoretical study of certain non-linear wave phenomena, Phil. Trans. Roy. Soc. 289 (1978) 373-404.
3. J.W. Miles, The Korteweg-de Vries equation: A historical essay, J. Fluid Mech. 106 (1981) 131-147.
4. D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. 39 (1985) 422-443.
5. I.S. Greig, J.L.L. Morris, A hopscotch method for the Korteweg-de Vries equation, J. Comp. Phys. 20 (1976) 64-80.
6. M.E. Alexander, J.L.L. Morris, Galerkin methods for some model equations for nonlinear dispersive waves, J. Comp. Phys. 30 (1979) 428-451.
7. N.J. Zabusky, A synergetic approach to problem of nonlinear dispersive wave propagation and interaction, in: W. Ames (Ed.), Proceedings of the Symposium on Non-linear Partial Differential Equations, Academic Press, New York, 1967, pp. 223-258.
8. C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura, Korteweg-de Vries equation and generalizations. VI. methods for exact solution, Comm. Pure Appl. Math. 27 (1974) 97-133.
9. K. Goda, On stability of some finite difference schemes for the Korteweg-de Vries equation, 3, Phys. Soc. Japan 39 (1975) 229-236.
10. A.C. Vliengenthart, On finite difference methods for the Korteweg-de Vries equation, J. Engrg. Math. 5 (1971) 137-155.
11. J.M.S. Serna, I. Christie, Petrov Galerkin methods for non linear dispersive waves, J. Comp. Phys. 39 (1981) 94-102.
12. S.W. Schoomie, Spline Petrov-Galerkin methods for the numerical solution of the Korteweg-de Vries equation, IMA J. Num. Anal. 2 (1982) 95-109.
13. L.R.T. Gardner, A.H.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 modelling and simulations, Istanbul, vol. 1C, 1988, pp. 81-93.
14. T.R. Taha, M.J. Ablowitz, Analytic and numerical aspects of certain non-linear evolution equations III. Numerical KdV Equation, J. Comp. Phys. 55 (1984) 231-253.
15. T.R. Goodman, Applications of integral methods to transient non-linear heat transfer, in: T.F. Irvine Jr., J.P. Harnett (Eds.), In Advances in Heat Transfer vol. 1, 1964, pp. 51-122.
16. D. Langford, The heat balance integral method, Int. J. Heat Mass Transfer 16 (1973) 2424-2428.
17. D.S. Riley, P.W. Duck, Application of the heat balance integral method to the freezing of a cuboid, Int. J. Heat Mass Transfer 20 (1977) 294-296.
18. A.S. Wood, An efficient finite-difference scheme for multidimensional Stefan problems, Int. J. Numer. Meth. Eng. 23 (1986) 1757-1771.
19. G.E. Bell, A refinement of the heat balance integral method applied to a melting problem, Int. J. Heat Mass Transfer 21 (1978) 1357-1362.
20. G.E. Bell, Solidification of a liquid about a cylindrical pipe, Int. J. Heat Mass Transfer 22 (1979) 1681-1686.
21. A. Özdeş, S. Kutluay, A.R. Bahadir, A. Şahin, A heat balance integral solution to Burger's equation in one space dimension, Balkan Phys. Lett. 4 (4) (1996) 251-256.