Numerical analysis of a first-order in time implicit-symplectic scheme for predator-prey systems

DOI10.1016/j.camwa.2017.04.030zbMath1390.92105OpenAlexW2616985254WikidataQ115580788 ScholiaQ115580788MaRDI QIDQ1643248

Fasma Diele, Marcus R. Garvie, Cǎ tǎ lin Trenchea

Publication date: 19 June 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.04.030

zbMATH Keywords

numerical schemesreaction-diffusion predator-prey systemssemi-discrete in time formulation

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (8)

A constructive method for parabolic equations with opposite orientations arising in optimal control ⋮ Stability and errors estimates of a second-order IMSP scheme ⋮ An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model ⋮ Sobolev gradients for segmentation of vector-valued texture images ⋮ \textit{GeCo}: geometric conservative nonstandard schemes for biochemical systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the Z-type control of backward bifurcations in epidemic models

Uses Software

• PRED_PREY

Cites Work

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• A second-order positivity preserving scheme for semilinear parabolic problems
• Devising efficient numerical methods for oscillating patterns in reaction-diffusion systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Simple finite element methods for approximating predator-prey dynamics in two dimensions using \texttt{MATLAB}
• On the positivity of Poisson integrators for the Lotka-Volterra equations
• Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB
• Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response
• IMEX Runge-Kutta schemes for reaction-diffusion equations
• A three level finite element approximation of a pattern formation model in developmental biology
• Spatiotemporal Complexity of Plankton and Fish Dynamics
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Spatial Ecology via Reaction‐Diffusion Equations
• Spatiotemporal dynamics of two generic predator–prey models
• Ecological chaos in the wake of invasion.
• Geometric Numerical Integration
• Partial Differential Equations
• IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics

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