One can generate an approximate deterministic trajectory by considering the
system of reactions as a set of ordinary differential equations and then
numerically integrating these equations to determine the reactions counts and
species populations. There are many schemes for numerically integrating
ODE's. The Cain solver uses the
<a href="http://en.wikipedia.org/wiki/Cash-Karp">Cash-Karp</a> variant
<a href="http://en.wikipedia.org/wiki/Runge-Kutta">Runge-Kutta</a> method.
This is a fifth-order explicit method with an adaptive step size.
There are also a number of solvers with fixed step size. These are primarily
useful for testing algorithms. The adaptive step size solver is preferred
for normal work.