A fast solver for systems of reaction-diffusion equations

Details A fast solver for systems of reaction-diffusion equations A fast solver for systems of reaction-diffusion equations

2001-02-27

arxiv.org/abs/math/0102218v1

Mathematics

Numerical Analysis

8 pages, 3 figures, to appear in Proc. 13th Domain Decomposition Conference, Lyon, October 2000

Scientific paper

In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, $\partial_t u + a \cdot \nabla u = \Delta u + F (x, t, u)$, $x \in \Omega \subset \mathbf{R}^3$, $t > 0$. Here, $u$ is a vector-valued function, $u \equiv u(x, t) \in \mathbf{R}^m$, $m$ is large, and the corresponding system of ODEs, $\partial_t u = F(x, t, u)$, is stiff. Typical examples arise in air pollution studies, where $a$ is the given wind field and the nonlinear function $F$ models the atmospheric chemistry.

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