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Symmetry
Volume 18
Issue 1
10.3390/sym18010176
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Article

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

by
Nihal Özdoğan
Faculty of Engineering and Natural Sciences, Department of Mathematics, Bursa Technical University, 16310 Bursa, Turkey
Symmetry 2026, 18(1), 176; https://doi.org/10.3390/sym18010176 (registering DOI)
Submission received: 21 November 2025 / Revised: 13 January 2026 / Accepted: 14 January 2026 / Published: 17 January 2026
(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)
Versions Notes

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.
Keywords: nonstandard finite difference (NSFD) theta schemes; competitive species model with toxicants; Jury conditions; unconditional stability; numerical consistency; ecological dynamics nonstandard finite difference (NSFD) theta schemes; competitive species model with toxicants; Jury conditions; unconditional stability; numerical consistency; ecological dynamics

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MDPI and ACS Style

Özdoğan, N. Unconditionally Stable Nonstandard Finite Difference Theta Schemes for Competitive Species Models with Toxicant Effects: A Jury Condition-Guaranteed Approach. Symmetry 2026, 18, 176. https://doi.org/10.3390/sym18010176

AMA Style

Özdoğan N. Unconditionally Stable Nonstandard Finite Difference Theta Schemes for Competitive Species Models with Toxicant Effects: A Jury Condition-Guaranteed Approach. Symmetry. 2026; 18(1):176. https://doi.org/10.3390/sym18010176

Chicago/Turabian Style

Özdoğan, Nihal. 2026. "Unconditionally Stable Nonstandard Finite Difference Theta Schemes for Competitive Species Models with Toxicant Effects: A Jury Condition-Guaranteed Approach" Symmetry 18, no. 1: 176. https://doi.org/10.3390/sym18010176

APA Style

Özdoğan, N. (2026). Unconditionally Stable Nonstandard Finite Difference Theta Schemes for Competitive Species Models with Toxicant Effects: A Jury Condition-Guaranteed Approach. Symmetry, 18(1), 176. https://doi.org/10.3390/sym18010176

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