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 RK2 and RK4, respectively), Euler method, and NSFD method presented in [1] indicate that the new methods have better accuracy and convergence.
