  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 accelerated stochastic simulation algorithms. Numerical
experiments compare the new methods with the established stochastic simulation
algorithm and the tau-leaping method.
