Hybrid method for the chemical master equation

Hybrid method for the chemical master equation

The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate...

Stochastic Hybrid System for Chemical Master Equation

A Discrete Spectral Method for the Chemical Master Equation

As an equivalent formulation of the Markov-assumption of stochastic processes, the master equation of chemical reactions is an accurate description of general systems in chemistry. ForD reacting species this is a differential-difference equation in D dimensions, exactly soluble for very simple systems only. We present and analyze a novel solution strategy based upon a Galerkin spectral method w...

An Adaptive Wavelet Method for the Chemical Master Equation

An adaptive wavelet method for the chemical master equation is constructed. The method is based on the representation of the solution in a sparse Haar wavelet basis, the time integration by Rothe’s method, and an iterative procedure which in each time-step selects those degrees of freedom which are essential for propagating the solution. The accuracy and efficiency of the approach is discussed,...

Improved Krylov-FSP Method for Solving the Chemical Master Equation

Model reduction techniques are needed to directly solve the chemical master equation (CME) due to its enormous size. We recently described an algorithm that solved the CME by combining the finite state projection, stochastic simulation algorithm and Krylov subspace approximations. In this work, we add further improvements that consist of an incomplete orthogonalization process with Krylov subsp...