2 research outputs found
Numerical convergence of a Telegraph Predator-Prey System
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.Comment: Submited to journal "Semina: Exact and Technological Sciences
Numerical convergence of a Telegraph Predator-Prey system
Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented