Unconditionally Stable Nonstandard Finite Difference Theta Schemes for Competitive Species Models with Toxicant Effects: A Jury Condition-Guaranteed Approach

Abstract

The paper attempts to propose nonstandard finite difference theta schemes to analyze solutions of a competitive problem with toxicants. We have seen that the competitive system is elementary-stable, and the stability features of each equilibrium point of the derived model are the same as those of the continuous model for any value of step size. Therefore, we can say that nonstandard finite difference theta schemes exhibit symmetry at every stage where stability analyses of the mathematical model are performed.