Nonstandard finite difference schemes with application to biological models

Abstract

This paper deals with the construction of nonstandard finite difference methods for solving a specific Rosenzweig-MacArthur predator-prey model. The reorganization of the denominator of the discrete derivatives and nonlocal approximations of nonlinear terms are used in the design of new schemes. We establish that the proposed nonstandard finite difference methods are elementary stable and satisfy the positivity requirement. We provide some numerical comparisons to illustrate our results.