Nonstandard finite difference method by nonlocal approximation

Mathematics and Computers in Simulation

Volumn 61, Issue 3-6, 2003, Pages 465-475

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

^a UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

Evolution equation; Nonlocal approximation; Nonstandard finite difference method

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EVOLUTION EQUATIONS;

FINITE DIFFERENCE METHOD;

EID: 0037472545     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(02)00106-4     Document Type: Conference Paper

References (11)

1. R. Anguelov, J.M.-S. Lubuma, On the Mathematical Foundation of the Nonstandard Finite Difference Method, in: B. Fiedler, K. Gröger, J. Sprekels (Eds.), Proceedings of the International Conference on Differential Equations, EQUADIFF'99, World Scientific, Singapore, 2000, pp. 1401-1403.
2. Anguelov R., Lubuma J.M.-S., On the nonstandard finite difference method, Keynote address at the Annual Congress of the South African Mathematical Society, Pretoria, South Africa, 16-18 October 2000. Notices S. Afr. Math. Soc. 31(3):2000;143-152.
3. Anguelov R., Lubuma J.M.-S., Contributions to the mathematics of the nonstandard finite difference method and applications. Num. Methods Partial Differential Equations. 17(5):2001;518-543.
4. D. Colton, Partial Differential Equations, An Introduction, Random House, New York, 1988.
5. H.V. Kojouharov, B.M. Chen, Nonstandard methods for advection-diffusion-reaction equations, in: R.E. Mickens (Ed.), Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000, pp. 55-108.
6. J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, New York, 1991.
7. R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
8. R.E. Mickens, Nonstandard finite difference schemes: a status report, in: Y.C. Teng, E.C. Shang, Y.H. Pao, M.H. Schultz, A.D. Pierce (Eds.), Theoretical and Computational Acoustics 97, World Scientific, Singapore, 1999, pp. 419-428.
9. R.E. Mickens (Ed.), Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
10. R.D. Richtmyer, K.W. Morton, Difference Methods for Initial Value Problems, Interscience, New York, 1967.
11. W. Walter, Ordinary Differential Equations, Springer, Berlin, 1998.