Research Article
Year 2016,
Volume: 4 Issue: 4, 27 - 32, 31.12.2016
Abstract
References
- R. Anguelov, J.M.-S. Lubuma, Nonstandard finite difference method by nonlocal approximation, Math. Comput. Simul. 61 (3-6) (2003) 465-475
- R. Anguelov, J.M.-S. Lubuma, On the Mathematical Foundation of the Nonstandard Finite Difference Method, in: B. Fiedler,
- K. Groger, J. Sprekels (Eds.), Proceedings of the International Conference on Differential Equations, EQUADIFF 99, World Scientific, Singapore, 2000, pp. 1401-1403
- R. Anguelov, J.M.-S. Lubuma, On the 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
- R. Anguelov, J.M.-S. Lubuma, Contributions to the Mathematics of the Nonstandard Finite Difference Method and Applications, Num. Methods Partial Differential Equations 17 (5) (2001) 518-543
- J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, Newyork, 1991
- R.D. Richtmyer, K.W. Morton, Difference Methods for Initial Value Problems, Interscience, New York, 1967
- R.E. Mickens (Ed.), Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
- R.E. Minkens, Nonstandard Finite Difference Schemes for Differential Equations, Journal of Difference Equations and Applications, 2002, 8:9, 823-847
- Larson, R. (2006). Calculus: An Applied Approach 9E. Boston: Brooks.
Year 2016,
Volume: 4 Issue: 4, 27 - 32, 31.12.2016
Abstract
In this paper, a powerful recent non-standard finite different method by nonlocal approximation is improved. Also, compared standard finite difference method to this non-standard finite different method in terms of stability and accuracy. As a numerical example, Hybrid Selection & Genetics equation is considered as the candidate from class of first order ODEs with polynomial right-hand sides. Furthermore, results obtained from the non-standard finite different method and MATLAB ODE solvers (ode15s,ode23s) compared in terms of stability, accuracy, and execution time.
References
- R. Anguelov, J.M.-S. Lubuma, Nonstandard finite difference method by nonlocal approximation, Math. Comput. Simul. 61 (3-6) (2003) 465-475
- R. Anguelov, J.M.-S. Lubuma, On the Mathematical Foundation of the Nonstandard Finite Difference Method, in: B. Fiedler,
- K. Groger, J. Sprekels (Eds.), Proceedings of the International Conference on Differential Equations, EQUADIFF 99, World Scientific, Singapore, 2000, pp. 1401-1403
- R. Anguelov, J.M.-S. Lubuma, On the 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
- R. Anguelov, J.M.-S. Lubuma, Contributions to the Mathematics of the Nonstandard Finite Difference Method and Applications, Num. Methods Partial Differential Equations 17 (5) (2001) 518-543
- J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, Newyork, 1991
- R.D. Richtmyer, K.W. Morton, Difference Methods for Initial Value Problems, Interscience, New York, 1967
- R.E. Mickens (Ed.), Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
- R.E. Minkens, Nonstandard Finite Difference Schemes for Differential Equations, Journal of Difference Equations and Applications, 2002, 8:9, 823-847
- Larson, R. (2006). Calculus: An Applied Approach 9E. Boston: Brooks.
There are 10 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 31, 2016 |
| Published in Issue | Year 2016 Volume: 4 Issue: 4 |