Numerical treatment of a nonlocal model for phytoplankton aggregation

In this paper, we are interested in the numerical treatment of a nonlinear model describing phytoplankton aggregation. The model consists in an integro-differential diffusion equation, with a chemotaxis term responsible for self-attraction of phytoplankton cells. We develop and implement a numerical scheme to solve this nonlinear PDE and present numerical solutions for parameters values corresponding to real conditions in nature. The numerical results emphasize the role of the nonlinear chemotaxis term in producing aggregating patterns and further, they are used to explore the asymptotic behavior of the model.