Analytical and Numerical Study of the Problem of the Plankton Population Dynamics in the Presence of Microplastics

This article studies and carries out a numerical implementation of a mathematical model of the dynamics of plankton populations in the presence of microplastic particles. The initial-boundary value problem of the dynamics of plankton populations and microplastics is formulated and the approach to linearize the continuous model under consideration is described. The results of a study of the proximity of solutions to the linearized and original initial-boundary value problems by the energy method are presented. The approximation of a continuous model of the dynamics of plankton populations with the second order of accuracy relative to the steps of the spatial grid with boundary conditions of the second and third kind is carried out. To numerically solve the problem, a software package is developed for modeling problems of biological kinetics, geochemical cycles, and microplastic transformation. A numerical experiment is carried out based on the developed software package.