NUMERICAL SIMULATIONS OF A NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION MODELING PHYTOPLANKTON AGGREGATION

Abstract

In this paper, we are interested in the numerical simulation of a nonlinear stochastic partial differential equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists of a diffusion equation with a chemotaxis term and a branching noise. We develop and implement a numerical scheme to solve this SPDE and present its numerical solutions for parameter values corresponding to real conditions in nature. Further, a comparison is made with two deterministic versions of the SPDE, that are advection–diffusion equations with linear and nonlinear reaction terms, to emphasize the efficiency of the stochastic equation in modeling the aggregation behavior in phytoplankton.