Galerkin Spectral Method Applied to the Chemical Master Equation  

作　　者：Stefan Engblom 

机构地区：[1]Department of Information Technology,Uppsala University,P.O.Box 337,SE-75105 Uppsala,Sweden

出　　处：《Communications in Computational Physics》2009年第5期871-896,共26页计算物理通讯（英文）

基　　金：The author is also indebted to Hermann Matthies for a long and valuable discussion during the IHP-EU Workshop“Breaking Complexity”in Bad Honnef,Germany.References[8,9,47,48]was kindly provided to the author by Peter Deuflhard and Michael Wulkow;Financial sup-port has been obtained from the Swedish National Graduate School in Mathematics and Computing.

摘　　要：Stochastic well-stirred chemically reacting systems can be accurately modeled by a continuous-time Markov-chain.The corresponding master equation evolves the 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 an inherent natural adaptivity and a very favorable choice of basis functions.Theoretical results related to convergence have been developed previously and are briefly summarized while implementation issues,including how to adapt the basis functions to follow the solution they represent,are covered in more detail here.The method is first applied to a model problem where the convergence can easily be studied.Then we take on two more realistic systems from molecular biology where stochastic descriptions are often necessary to explain experimental data.The conclusion is that,for sufficient accuracy demands and not too high dimensionality,the method indeed provides an alternative to other methods.

关 键 词：Master equation spectral-Galerkin method high dimensional problem moving basis chemical reactions 

分 类 号：O17[理学—数学]