Numerical convergence of a Telegraph Predator-Prey System

TL;DR

This paper investigates the numerical convergence and stability of a Telegraph Predator-Prey PDE system, analyzing how mesh refinement and parameters influence stability through discretization and von Neumann stability conditions.

Contribution

It introduces a discretization approach for the Telegraph Predator-Prey system and analyzes its stability conditions considering reactive, diffusive, and delay effects.

Findings

Mesh refinement affects stability outcomes.

Model parameters influence stability and instability.

Discretization consistency was verified.

Abstract

The numerical convergence of a Telegraph Predator-Prey system is studied. This system of partial differential equations (PDEs) can describe various biological systems with reactive, diffusive and delay effects. Initially, our problem is mathematically modeled. Then, the PDEs system is discretized using the Finite Difference method, obtaining a system of equations in the explicit form in time and implicit form in space. The consistency of the Telegraph Predator-Prey system discretization was verified. Next, the von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Telegraph system with delay. For our Telegraph Predator-Prey system, through numerical experiments, it was verified tat the mesh refinement and the model parameters (reactive constants, diffusion coefficient and delay term) determine the stability/instability conditions of the model. Keywords: Telegraph-Diffusive-Reactive System. Maxwell-Cattaneo Delay. Discretization Consistency. Von Neumann Stability. Numerical Experimentation.