Spectral approximation of solutions to the chemical master equation
Spectral approximation of solutions to the chemical master equation
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DOI：
10.1016/j.cam.2008.10.029
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发表时间：
2009-07-01
影响因子：
2.4
通讯作者：
Engblom, Stefan
中科院分区：
文献类型：
--
作者：
Engblom, Stefan
化学反应的主方程是化学中一般系统的精确随机描述。对于D种反应，这是D维的微分-差分方程。只对非常简单的系统完全可溶。我们提出并分析了一种新的求解策略，即具有良好基函数选择的伽辽金谱法。建立了相应空间的谱近似理论，并讨论了稳定性问题。通过两个已知解的模型问题和一个未知解的第三个模型问题的数值解，证明了该方法的收敛性。结果表明，该方法是有效的、准确的，在维数不太高的情况下，为其他求解方法提供了一种可行的选择。(C) 2008 Elsevier B.V.版权所有
The master equation of chemical reactions is an accurate stochastic 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 propose and analyze a novel solution strategy in the form of a Galerkin spectral method with a favorable choice of basis functions. A spectral approximation theory in the corresponding spaces is developed and the issue of stability is discussed.The convergence properties of the method are demonstrated by the numerical solution of two model problems with known solutions and a third problem for which no solution is known. It is shown that the method is effective and accurate, providing a viable alternative to other solution methods when the dimensionality is not too high. (C) 2008 Elsevier B.V. All rights reserved.