A model for fast computer simulation of waves in excitable media
Selcted papers from a meeting on Waves and pattern in chemical and biological media
Mathematical physiology
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A multidomain spectral method for supersonic reactive flows
Journal of Computational Physics
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
Journal of Computational Physics
Journal of Computational Physics
Spiral waves on static and moving spherical domains
Journal of Computational and Applied Mathematics
A pseudospectral method of solution of Fisher's equation
Journal of Computational and Applied Mathematics
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Journal of Scientific Computing
The spectral methods for parabolic Volterra integro-differential equations
Journal of Computational and Applied Mathematics
A Lattice Boltzmann Model for the Reaction-Diffusion Equations with Higher-Order Accuracy
Journal of Scientific Computing
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We present a study of the convergence of different numerical schemes in the solution of the Fitzhugh-Nagumo equations in the form of two coupled reaction diffusion equations for activator and inhibitor variables. The diffusion coefficient for the inhibitor is taken to be zero. The Fitzhugh-Nagumo equations, have spatial and temporal dynamics in two different scales and the solutions exhibit shock-like waves. The numerical schemes employed are a Chebyshev multidomain method, a finite difference method and the method developed by Barkley [D. Barkley, A model for fast computer simulation of excitable media, Physica D, 49 (1991) 61-70]. We consider two different models for the local dynamics. We present results for plane wave propagation in one dimension and spiral waves for two dimensions. We use an operator splitting method with the Chebyshev multidomain approach in order to reduce the computational time. Zero flux boundary conditions are imposed on the solutions.