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Positivity preserving and elementary stable nonstandard finite difference scheme for the predator-prey model

M. Mehdizadeh Khalsaraei , Sh. Heydari, L. Davari Algoo, R. Shokri Jahandizi


A nonstandard finite difference scheme for a class of predator-prey model is proposed. Computationally a simple explicit scheme is derived by using the nonlocal approximation of the nonlinear terms. Also renormalization of the denominator of the discrete derivatives are used for the proposed scheme. This approach leads to a significant qualitative improvements in the behavior of the numerical solution. Unlike the standard explicit methods, the
new scheme preserves the stability of the equilibriums and the positivity requirement of solutions.


Predator-prey, Stability, Positivity, Elementary stable, Nonstandard finite difference.

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