APPROXIMATE EXPONENTIAL ALGORITHMS TO SOLVE THE CHEMICAL MASTER EQUATION

Approximate Exponential Algorithms to Solve the Chemical Master Equation

This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accele...

Approximate probability distributions of the master equation.

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of wh...

A graph-based approach for the approximate solution of the chemical master equation.

The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution—which gives the corresponding probability density function—is possible only in very simple cases; there is a clear need for approximation techniques. Here, we propose a novel perturbative three-step approach, which draws heavily on graph th...

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...

Numerical Methods for the Chemical Master Equation