Numerical solutions of a mathematical model of plankton–oxygen dynamics using a meshless method

Shirzadi, Ahmad; Ghayedi, Shabnam; Safarpoor, Mansour; Bagheri Bardi, Ghorbanali

doi:10.22055/jamm.2018.13726

Numerical solutions of a mathematical model of plankton–oxygen dynamics using a meshless method

Document Type : Original Paper

Authors

Ahmad Shirzadi ¹

Shabnam Ghayedi ²

Mansour Safarpoor ¹

Ghorbanali Bagheri Bardi ²

¹ Department of Mathematics, Persian Gulf University, Bushehr, Iran.

² Department of Mathematics, Persian Gulf University, Bushehr, Iran

10.22055/jamm.2018.13726

Abstract

This paper is concerned with the numerical solutions of a mathematical model of coupled plankton–oxygen dynamics. About 70% of the atmospheric oxygen is produced by the photosynthetic activity of phytoplankton and the phytoplankton activities are affected by the ocean dynamics. So, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. A mode describing plankton–oxygen dynamics is considered. For discretizing the model which is a system of nonlinear differential equations, a combination of finite differences and meshless methods are used. The time variable is discretized by forward finite difference scheme. Because of the high accuracy of meshless methods, in the space dependent model, a meshless approach is proposed for discretizing the space variable. The method uses the strong form equation and collocation approach for discretization. Multiquadrics radial basis functions are used which have the approximation power of exponential order. Numerical results reveal that in a specific domain of oxygen production the model is stable. Also, it is shown that global warming will affect the system, resulting in the oxygen reduction and plankton extinction.

Keywords

Plankton

Global warming

Differential equations

Finite difference methods

Meshless methods

Subjects