Positive and elementary stable nonstandard numerical methods with applications to predator-prey models

Journal of Computational and Applied Mathematics

Volumn 189, Issue 1-2, 2006, Pages 98-108

  Dimitrov, Dobromir T ^a   Kojouharov, Hristo V ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Elementary stable; Finite difference; Nonstandard; Positive; Predator prey

Indexed keywords

IMPROVEMENT; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; STANDARDIZATION;

ELEMENTARY STABLE; FINITE-DIFFERENCE; NONSTANDARD; POSITIVE; PREDATOR-PREY;

NUMERICAL METHODS;

EID: 31544467830     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.04.003     Document Type: Conference Paper

References (17)

1. R. Anguelov, P. Kama, and J.M.-S. Lubuma On non-standard finite difference models of reaction-diffusion equations J. Comput. Appl. Math. 175 1 2005 11 29
2. R. Anguelov, and J.M.-S. Lubuma Contributions to the mathematics of the nonstandard finite difference method and applications Numer. Methods Partial Differential Equations 17 5 2001 518 543
3. R. Anguelov, and J.M.-S. Lubuma Nonstandard finite difference method by nonlocal approximation Math. Comput. Simul. 61 3-6 2003 465 475
4. F. Brauer, and C. Castillo-Chavez Mathematical Models in Population Biology and Epidemiology 2001 Springer New York
5. H. Burchard, E. Deleersnijder, and A. Meister A high-order conservative Patankar-type discretization for stiff systems of production-destruction equations Appl. Numer. Math. 47 1 2003 1 30
6. E.A. Coddington, and N. Levinson Theory of Ordinary Differential Equations 1984 Krieger Florida
7. D.T. Dimitrov, H.V. Kojouharov, Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss, Math. Comput. Simul., 2005, in press.
8. D.T. Dimitrov, and H.V. Kojouharov Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems Appl. Math. Lett. 18 7 2005 769 774
9. A.B. Gumel, R.E. Mickens, and B.D. Corbett A non-standard finite-difference scheme for a model of HIV transmission and control J. Comput. Methods Sci. Eng. 3 1 2003 91 98
10. C.S. Holling The functional response of predators to prey density and its role in mimicry and population regulation Mem. Entomol. Soc. Canada 45 1965 1 60
11. H. Jansen, and E.H. Twizell An unconditionally convergent discretization of the SEIR model Math. Comput. Simul. 58 2002 147 158
12. J.M.-S. Lubuma, and A. Roux An improved theta-method for systems of ordinary differential equations J. Differential Equations Appl. 9 11 2003 1023 1035
13. A.S. de Markus, and R.E. Mickens Suppression of numerically induced chaos with nonstandard finite difference schemes J. Comput. Appl. Math. 106 2 1999 317 324
14. R.E. Mickens Nonstandard Finite Difference Model of Differential Equations 1994 World Scientific Singapore
15. R.E. Mickens Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation Numer. Methods Partial Differential Equations 13 1 1997 51 55
16. R.E. Mickens Nonstandard finite difference schemes for differential equations J. Differential Equations Appl. 8 9 2002 823 847
17. W. Piyawong, E.H. Twizell, and A.B. Gumel An unconditionally convergent finite-difference scheme for the SIR model Appl. Math. Comput. 146 2003 611 625