An adaptive method of lines solution of the Korteweg-de Vries equation

Computers and Mathematics with Applications

Volumn 35, Issue 12, 1998, Pages 13-25

  Saucez, P ^a   Vande Wouwer, A ^a   Schiesser, W E ^b  

^a FACULTÉ POLYTECHNIQUE DE MONS   (Belgium)

^b LEHIGH UNIVERSITY   (United States)

Author keywords

Numerical method of lines; Partial differential equations

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

EQUIDISTRIBUTION PRINCIPLE; KORTEWEG-DE VRIES EQUATION; METHOD OF LINES;

ADAPTIVE ALGORITHMS;

EID: 0032094380     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00093-5     Document Type: Article

References (14)

1. G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York, (1974).
2. F.D. van Niekerk and A. van Niekerk, A hermite rational approximation method for the Korteweg-de Vries equation, Mathl. Comput. Modelling 13 (5), 63-70, (1990).
3. J.M. Sanz-Serna and V.S. Manoranjan, A method for the integration in time of certain partial differential equations, J. Comp. Phys. 52, 273-289, (1983).
4. T.H. Taha and M.J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation, J. Comput. Phys. 35, 231, (1984).
5. W.E. Schiesser, Method of lines solution of the Korteweg-de Vries equation, Computers Math. Applic. 28 (10-12), 147-154, (1994).
6. G.E. Forsythe, M.A. Malcom and C.B. Moler, Computer Methods for Mathematical Computations, Prentice Hall, Englewood Cliffs, NJ, (1977).
7. P. Saucez, A. Vande Wouwer and W.E. Schiesser, Some observations on a static spatial remeshing method based on equidistribution principles, J. Comp. Phys. 128, 274-288, (1996).
8. B. Fornberg, Generation of finite difference formulas on arbitrarily spaced grid, Math. Comp. 51, 699-706, (1988).
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, (1991).
10. J.M. Sanz-Serna and I. Christie, A simple adaptive technique for nonlinear wave problems, J. Comp. Phys. 67, 348-360, (1986).
11. J.G. Blom and P.A. Zegeling, Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations, ACM Trans. Math. Software 20, 194-214, (1994).
12. W. Huang and R.D. Russell, A moving collocation method for solving time dependent partial differential equations, Appl. Num. Math. (to appear).
13. A. Vande Wouwer, P. Saucez and W.E. Schiesser, Some user-oriented insights into adaptive grid methods for partial differential equations in one space dimension, (submitted).
14. W.E. Schiesser, The Numerical Method of Lines, Academic Press, San Diego, CA, (1991).