# ODE Integration

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 Cash-Karp variant of the Runge-Kutta 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.