Asynchronous algorithm for integration of reaction-diffusion equations for inhomogeneous excitable media

Abstract

An asynchronous algorithm for the integration of reaction-diffusion equations for inhomogeneous excitable media is described. Since many physical systems are inhomogeneous where either the local kinetics or the diffusion or conduction properties vary significantly in space, integration schemes must be able to account for wide variations in the temporal and spatial scales of the solutions. The asynchronous algorithm utilizes a fixed spatial grid and automatically adjusts the time step locally to achieve an efficient simulation where the errors in the solution are controlled. The scheme does not depend on the specific form of the local kinetics and is easily applied to systems with complex geometries. © 2000 American Institute of Physics.