Dynamically Consistent NSFD Methods for Predator-prey System

In this paper, we introduce two nonstandard finite difference (NSFD) methods for solving the mathematical model of the Rosenzweig-MacArthur predator-prey system. These new proposed numerical methods have important features such as positivity and elementary stability. Numerical comparisons between the proposed methods and the other methods such as second-order and forth order Runge-Kutta methods (we refer them RK۲ and RK۴, respectively), Euler method, and NSFD method presented in [۶] indicate that the new methods have better accuracy and convergence.

Keywords:

Predator-prey , Stability , positivity , Elementary stable , Nonstandard Finite Difference‎