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A discrete spectral method for the chemical master equation

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. ForD 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 based upon a Galerkin spectral method with an inherent natural adaptivity and a very favorable choice of basis functions. The method is demonstrated by the numerical solution of two model problems followed by two more realistic systems taken from molecular biology. It is shown that the method remains effective and accurate, providing a viable alternative to other solution methods when the dimensionality is not too high.