Paper Info
Title
Numerical analysis of a first-order in time implicit-symplectic scheme for predator-prey systems.
Abstract
The numerical solution of reaction–diffusion systems modelling predator–prey dynamics using implicit-symplectic (IMSP) schemes is relatively new. When applied to problems with chaotic dynamics they perform well, both in terms of computational effort and accuracy. However, until the current paper, a rigorous numerical analysis was lacking. We analyse the semi-discrete in time approximations of a first-order IMSP scheme applied to spatially extended predator–prey systems. We rigorously establish semi-discrete a priori bounds that guarantee positive and stable solutions, and prove an optimal a priori error estimate. This analysis is an improvement on previous theoretical results using standard implicit–explicit (IMEX) schemes. The theoretical results are illustrated via numerical experiments in one and two space dimensions using fully-discrete finite element approximations.
Year
DOI
Venue
2017
10.1016/j.camwa.2017.04.030
Computers & Mathematics with Applications
Keywords
Field
DocType
Reaction–diffusion predator–prey systems,Semi-discrete in time formulation,Numerical schemes
Mathematical optimization,Mathematical analysis,First order,A priori and a posteriori,Symplectic geometry,Approximations of π,Finite element approximations,Numerical analysis,Chaotic,Mathematics
Journal
Volume
Issue
ISSN
74
5
0898-1221
Citations 
PageRank 
References 
0
0.34
5
Authors
3
Name
Order
Citations
PageRank
Fasma Diele100.34
Marcus R. Garvie2285.09
Catalin Trenchea3489.69