Licentiate thesis 2006-007

Numerical Methods for the Chemical Master Equation

Stefan Engblom

27 September 2006


The numerical solution of chemical reactions described at the meso-scale is the topic of this thesis. This description, the master equation of chemical reactions, is an accurate model of reactions where stochastic effects are crucial for explaining certain effects observed in real life. In particular, this general equation is needed when studying processes inside living cells where other macro-scale models fail to reproduce the actual behavior of the system considered.

The main contribution of the thesis is the numerical investigation of two different methods for obtaining numerical solutions of the master equation.

The first method produces statistical quantities of the solution and is a generalization of a frequently used macro-scale description. It is shown that the method is efficient while still being able to preserve stochastic effects.

By contrast, the other method obtains the full solution of the master equation and gains efficiency by an accurate representation of the state space.

The thesis contains necessary background material as well as directions for intended future research. An important conclusion of the thesis is that, depending on the setup of the problem, methods of highly different character are needed.

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