Stable Periodic Bifurcations of an Explicit Discretization of a Nonlinear Partial Differential Equation in Reaction Diffusion

DOI10.1093/imanum/8.4.435zbMath0664.65100OpenAlexW2043510793WikidataQ115275222 ScholiaQ115275222MaRDI QIDQ3814686

A. R. Mitchell, D. F. Griffiths

Publication date: 1988

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/8.4.435

zbMATH Keywords

stabilityNumerical examplesreaction diffusionexplicit discretizationstable periodic bifurcations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Related Items

On spurious fixed points of Runge-Kutta methods, Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay, Dynamics of constant and variable stepsize methods for a nonlinear population model with delay, Nonlinear diffusion and stable period 2 solutions of a discrete reaction- diffusion model, Global spectral analysis: review of numerical methods, NUMERICAL SOLUTION OF NONLINEAR EQUATION TO COMBINED DETERMINISTIC AND NARROW-BAND RANDOM EXCITATION, 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, Numerical solution of a nonlinear reaction-diffusion equation, Upper Semicontinuity of Attractors for Linear Multistep Methods Approximating Sectorial Evolution Equations, Law of large numbers for a general system of stochastic differential equations with global interaction, Partially implicit schemes for the numerical solutions of some nonlinear differential equations, Numerical solution of Hamiltonian systems in reaction-diffusion by symplectic difference schemes