Contributions to the mathematics of the nonstandard finite difference method and applications

Numerical Methods for Partial Differential Equations

Volumn 17, Issue 5, 2001, Pages 518-543

  Anguelov, Roumen ^a   Lubuma, Jean M S ^b  

^a VISTA UNIVERSITY   (South Africa)

^b UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Elementary stability; Nonstandard finite differences; Schemes preserving physical properties

Indexed keywords

EID: 0035449292     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.1025     Document Type: Article

References (20)

1. G. E. Forsythe and W. R. Wasow, Finite-difference methods for partial differential equations, Wiley, New York, 1960.
2. A. R. Mitchell and D. F. Griffiths, The finite difference method in partial differential equations, Wiley, New York, 1980.
3. R. D. Richtmyer and K. W. Morton, Difference methods for initial-value problems, Interscience, New York, 1967.
4. n, Part 1, Volume 1, North-Holland, Amsterdam, 1990.
5. K. W. Morton and D. F. Mayer, Numerical solution of partial differential equations, Cambridge University Press, Cambridge, 1994.
6. J. D. Lambert, Numerical methods for ordinary differential systems, Wiley, New York, 1991.
7. A. M. Stuart and A. R. Humphries, Dynamical systems and numerical analysis, Cambridge University Press, Cambridge, 1998.
8. R. E. Mickens, Nonstandard finite difference models of differential equations, World Scientific, Singapore, 1994.
9. R. E. Mickens, editor, Applications of nonstandard finite difference schemes, World Scientific, Singapore, 2000.
10. R. E. Mickens, Nonstandard finite difference schemes: a status report. In: Y. C. Teng, E. C. Shang, Y. H. Pao, M. H. Schultz, and A. D. Pierce, editors, Theoretical and computational accoustics 97, World Scientific, Singapore 1999, pp. 419-428.
11. H. V. Kojouharov and B. M. Chen, Nonstandard methods for the convective-dispersive transport equation with nonlinear reactions, Numer Methods Partial Differential Eq 15 (1999), 617-624.
12. R. E. Mickens, Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation, Numer Methods Partial Differential Eq 13 (1997), 51-55.
13. R. E. Mickens, Exact finite difference schemes for two-dimensional advection equations, J Sound Vib 207 (1997), 426-428.
14. R. E. Mickens, Asymptotic properties of solutions to two discrete Airy equations, J Difference Eq Appl 3 (1998), 231-239.
15. R. E. Mickens, Nonstandard finite difference scheme for a scalar reaction-convection PDE, J Difference Eq Appl 3 (1998), 359-367.
16. R. E. Mickens and K. O. Oyedeji, Numerical integration of the dissipative complex equation, Int J Appl Sci Comp 4 (1997), 99-103.
17. G. W. Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
18. J.C. Butcher, The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods, Wiley, New York, 1987.
19. W. Gautschi, Numerical solution of ordinary differential equations based on trigonometric polynomals, Numer Math 3 (1961), 381-397.
20. H. B. Keller, Approximation methods for nonlinear problems with applications to two-point boundary value problems, Math Comp 29 (1975), 464-474.