Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE
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Publication:1873331
DOI10.1016/S0021-9991(03)00004-4zbMath1019.65069MaRDI QIDQ1873331
Christopher E. Elmer, Erik S. Van Vleck
Publication date: 20 May 2003
Published in: Journal of Computational Physics (Search for Journal in Brave)
error analysistraveling wavesNagumo equationspatial and temporal discretizationbistable partial differential equation
Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)
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Cites Work
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- Existence of traveling wavefront solutions for the discrete Nagumo equation
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- Multidimensional nonlinear diffusion arising in population genetics
- Traveling waves in lattice dynamical systems
- Mathematical physiology
- The Fredholm alternative for functional-differential equations of mixed type
- The global structure of traveling waves in spatially discrete dynamical systems
- Introduction to functional differential equations
- Thermodynamically-consistent phase-field models for solidification
- Algorithms for phase field computation of the dendritic operating state at large supercoolings
- Nagumo's equation
- Traveling Wave Solutions for Bistable Differential-Difference Equations with Periodic Diffusion
- Long-Time Behavior of a Class of Biological Models
- Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
- Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability
- Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
- Existence and Stability of Multiple Impulse Solutions of a Nerve Equation
- Stability of Traveling Wavefronts for the Discrete Nagumo Equation
- Jacobi Iteration in Implicit Difference Schemes for the Wave Equation
- Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice
- Analysis and computation of travelling wave solutions of bistable differential-difference equations
- Dynamics of monotone travelling fronts for discretizations of Nagumo PDEs
- Computation of Mixed Type Functional Differential Boundary Value Problems
- Multiple impulse solutions to McKean's caricature of the nerve equation. I—existence