Adaptive treatment of polyreactions in weighted sequence spaces
IMPACT of Computing in Science and Engineering
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
A solver for the stochastic master equation applied to gene regulatory networks
Journal of Computational and Applied Mathematics
Solving chemical master equations by adaptive wavelet compression
Journal of Computational Physics
Hybrid numerical solution of the chemical master equation
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
An Adaptive Wavelet Method for the Chemical Master Equation
SIAM Journal on Scientific Computing
| Hi-index | 7.30 |
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.