Computation of Traveling Wave Solutions for Spatially
Discrete Bistable Reaction-Diffusion Equations
Abstract
Traveling wave solutions for reaction-diffusion equations on a
discrete spatial domain are considered. Traveling wave equations are
derived for the spatial domain Z^n for n=1,2,3. Using an idealized
nonlinear term, the anisotropy introduced by the lattice is analyzed.
Numerical techniques for solving the traveling wave equations
are introduced. Finally, some numerical experiments are presented.
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Analysis and Computation of Traveling Wave Solutions
of Bistable Differential-Difference Equations
Abstract
We consider
traveling wave solutions
to a class of differential-difference
equations.
Our interest is in understanding propagation failure, directional
dependence due to the discrete Laplacian, and the relationship between traveling wave solutions of the spatially continuous and spatially discrete
limits of this equation. The differential-difference equations that we study
include damped and undamped nonlinear wave and reaction-diffusion
equations as well as their spatially discrete
counterparts. Both analytical and numerical results are given.
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