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
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Journal of Scientific Computing
Noise-induced oscillations in an actively mode-locked laser
Computers & Mathematics with Applications
A Lax equivalence theorem for stochastic differential equations
Journal of Computational and Applied Mathematics
Runge-Kutta methods for jump-diffusion differential equations
Journal of Computational and Applied Mathematics
Higher Order Pathwise Numerical Approximations of SPDEs with Additive Noise
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Computing Stochastic Traveling Waves
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
Effects of noise on models of spiny dendrites
Journal of Computational Neuroscience
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We discuss the numerical solution of a number of stochastic perturbations of the Barkley model of excitable media, widely used in the study of spiral waves. Two numerical methods are considered for solving this equation, one based on Barkley's original formulation and one based on spectral methods. It is found to be beneficial to modify the nonlinearity describing the reaction kinetics. An efficient method of approximating the Wiener process is presented. The effectiveness of the methods depends on the stochastic PDE under consideration.