Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay

DOI10.1016/0168-9274(95)00051-UzbMath0834.65079MaRDI QIDQ1902072

Desmond J. Higham, Tasneem K. Sardar

Publication date: 10 April 1996

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityfixed pointsdelayevolution equationbifurcationpopulation dynamicsnonlinear reaction-diffusion equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) General theory of functional-differential equations (34K05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

LMI approach to exponential stability and almost sure exponential stability for stochastic fuzzy Markovian-jumping Cohen-Grossberg neural networks with nonlinear \(p\)-Laplace diffusion, On convergence of difference schemes for delay parabolic equations, Almost periodic solutions of partial differential equations with delay, Numerical bifurcation of a delayed diffusive food‐limited model with Dirichlet boundary condition, Convergence and stability analysis of the \({\theta}\)-method for delayed diffusion mathematical models, Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay, Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with \(p\)-Laplace diffusion and partially known transition rates via a differential inequality, Dynamics of constant and variable stepsize methods for a nonlinear population model with delay, A linearized compact difference scheme for a class of nonlinear delay partial differential equations, Unconditionally stable difference methods for delay partial differential equations, Discontinuous Galerkin time stepping for semilinear parabolic problems with time constant delay, LMI approach to stability analysis of Cohen-Grossberg neural networks with \(p\)-Laplace diffusion, A Posteriori Error Analysis for Crank--Nicolson--Galerkin Type Methods for Reaction-Diffusion Equations with Delay, Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay, Well-posedness of delay parabolic difference equations, Perpetual points and hidden attractors in dynamical systems, Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations, \(D\)-convergence of general linear methods for stiff delay differential equations, A boundedness-preserving finite-difference scheme for a damped nonlinear wave equation, Asymptotic stability of numerical methods for linear delay parabolic differential equations, Delay-dependent exponential stability for nonlinear reaction-diffusion uncertain Cohen-Grossberg neural networks with partially known transition rates via Hardy-Poincaré inequality, Asymptotic stability analysis of the linear θ-method for linear parabolic differential equations with delay, Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay, Open issues in devising software for the numerical solution of implicit delay differential equations, Delay-dependent elliptic reconstruction and optimal 𝐿^{∞}(𝐿²) a posteriori error estimates for fully discrete delay parabolic problems, Exact and numerical stability analysis of reaction-diffusion equations with distributed delays

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I: The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics
• Exponentially growing solutions for a delay-diffusion equation with negative feedback
• Island chain models and gradient systems
• Equilibrium states of adaptive algorithms for delay differential equations
• Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay
• Equilibrium states of Runge Kutta schemes
• Stable Periodic Bifurcations of an Explicit Discretization of a Nonlinear Partial Differential Equation in Reaction Diffusion
• The Dynamics of the Theta Method
• On spurious asymptotic numerical solutions of explicit Runge-Kutta methods
• Does Error Control Suppress Spuriosity?