Galerkin Spectral Method Applied to the Chemical Master Equation (Communications in Computational Physics, 2009)
Stochastic well-stirred chemically reacting systems can be accurately modeled by a continuous-time Markov-chain. The corresponding master equation evolvesthe system's probability density function in time but can only rarely be explicitly solved.We investigate a numerical solution strategy in the form of a spectral method with aninherent natural adaptivity and a very favorable choice of basis functions. Theoreticalresults related to convergence have been developed previously and are briefly summarized while implementation issues, including how to adapt the basis functions tofollow the solution they represent, are covered in more detail here.The method is first applied to a model problem where the convergence can easily bestudied. Then we take on two more realistic systems from molecular biology wherestochastic descriptions are often necessary to explain experimental data. The conclusion is that, for sufficient accuracy demands and not too high dimensionality, themethod indeed provides an alternative to other methods.