هدى رياض سلطان المالكي

This study presents a numerical simulation of a nonlinear predator-prey system described by a reaction diffution 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 mumerical 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.

.This study consists of a mathematical analysis of the predators-preys system convex domain lambda subset \mathbb{R} ^ a * (d = 1, 2, 3) with Robin boundary. conditions. The strong solution for this and is unique, it's requiring stringent conditions on the initial data to achieve high regularity. As shown in this study the continuous dependence of the strong solution on the initial conditions in Sobolev space

A convex open boundary domain was used to define the predator-prey equations. This was then mathematically analysed using Robin boundary conditions. Using the Faedo-Galerkin methodology and compactness arguments, we demonstrate the existence of strong and weak solutions and their uniqueness. The solution findings exhibit a higher level of regularity. We construct a more regular model based on the initial data. Furthermore, we can demonstrate continuous dependence on initial conditions. To complement the theoretical results, numerical simulations were also conducted, confirming the validity of the model and illustrating the dynamic behavior of the predator-prey system under Robin boundary conditions.