Computation of traveling waves for spatially discrete bistable reaction-diffusion equations
type: Item
instance of: scholarly article
title: Computation of traveling waves for spatially discrete bistable reaction-diffusion equations
zbMATH Open document ID: 0856.65116
DOI: 10.1016/0168-9274(95)00123-9
author: Christopher E. Elmer
author: E. Van Vleck
published in: Applied Numerical Mathematics
publication date: 1996-07-07T00:00:00Z
review text: The authors analyze an idealized system of bistable reaction-diffusion equations with spatial domain \(Z^n\), \(n=1,2,3\). The equations for traveling wave solutions are derived. These equations have the form of differential difference two-point boundary problems defined on the real line. Using an idealized nonlinear term, the lattice induced anisotropy is analyzed. Numerical methods for computing the traveling waves directly are presented. They include the use of monotone interpolants for a collocation scheme, the use of asymptotic boundary conditions and a phase condition. Finally, some numerical experiments are presented.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 897536
zbMATH Keywords: lattice anisotropy
zbMATH Keywords: propagation failure
zbMATH Keywords: system of bistable reaction-diffusion equations
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: differential difference two-point boundary problems
zbMATH Keywords: collocation
zbMATH Keywords: numerical experiments
reviewed by: L. Vázquez
describes a project that uses: pchip
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00123-9
OpenAlex ID: W2131957522
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description: scientific article; zbMATH DE number 897536