Numerical Simulation of a Nonlinear Predator-Prey System with Robin Boundary Conditions

Abstract

This study presents a numerical simulation of a nonlinear predator-prey system described by a reaction-diffusion model within a convex, open domain, subject to Robin boundary conditions. The Finite Element Method (FEM) is employed to discretize and solve the system, offering a practical approach to capture the spatiotemporal dynamics of predator-prey interactions. Furthermore, an error estimation is derived to evaluate the accuracy of the numerical approximation in comparison to the exact continuous solution. The results confirm the reliability and efficiency of the proposed numerical scheme, particularly in handling the complexities introduced by the Robin boundary conditions.