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 oxygenplankton 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. Similar results for stability are obtained in both continuous and discrete models. The model is solved by the RungeKutta–Fehlberg (RKF45) method, and the numerical results are compared in graphical forms. Moreover, the comparison of numerical results obtained by the NSFD method, the Euler method and the fourth order Runge-Kutta (RK4) method is presented in tabular form. Furthermore, the efficiency of the NSFD method compared to classical methods such as the Euler method and the RK4 method for the bigger step sizes is shown in tabular forms.