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

Authors:
Dobromir T. Dimitrov;Hristo V. Kojouharov
Affiliations:
Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA;Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous predator-prey models, are formulated and analyzed. The proposed numerical techniques are based on a nonlocal modeling of the growth-rate function and a nonstandard discretization of the time derivative. This approach leads to significant qualitative improvements in the behavior of the numerical solution. Applications of the PESN methods to a specific Rosenzweig-MacArthur predator-prey model are also presented.