A Nonstandard Finite Difference Scheme for a Mathematical Model Presenting the Climate Change on the Oxygen-plankton System

Abstract

This paper presents a mathematical model describing climate change in the oxygen-plankton system. The model consists of a system of non-linear ordinary differential equations. The Nonstandard Finite Difference (NSFD) method is applied to discretize the non-linear system. The stability of the continuous and discrete model is presented for the given parameters in the literature. The compatibility of the results has been seen. Moreover, the model is solved by both the NSFD method and the Runge–Kutta–Fehlberg (RKF45) method. The numerical results are compared. Furthermore, the efficiency of the NSFD method compared to classical methods such as the Euler method and the fourth order Runge-Kutta (RK4) method for the bigger step size is shown in tabular form.

Keywords

• Nonstandard Finite Difference Method
• Oxygen-plankton System
• Stability Analysis
• Schur-Cohn criterion

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