A Discrete Spectral Method for the Chemical Master Equation

Stefan Engblom

June 2006

Abstract:

As an equivalent formulation of the Markov-assumption of stochastic processes, the master equation of chemical reactions is an accurate description of general systems in chemistry. For D reacting species this is a differential-difference equation in D dimensions, exactly soluble for very simple systems only.

We present and analyze a novel solution strategy in the form of a Galerkin spectral method with an inherent natural adaptivity and a very favorable choice of basis functions.

The method is exemplified by the numerical solution of two systems taken from molecular biology. It is shown that the method remains effective and accurate when other traditional solution methods produce less useful results.

Note: Superseded by report nr 2008-005

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