COPASI supports three different methodologies to calculate a trajectory. The first method is to do a deterministic time course simulation of your model using the LSODA (or LSODAR if events are being used) [Petzold83] algorithm. For systems with small particle numbers, it is sometimes better to do a stochastic simulation rather than a deterministic one. COPASI supports several methods for the stochastic calculation of time series: the next reaction method described by Gibson and Bruck [Gibson00], the direct method [Gillespie76], tau leaping [Gillespie01] and adaptive SSA [Cao07].

Since the deterministic simulation is inappropriate for some systems but on the other hand, the stochastic simulation is too time consuming, there are some methods that try to combine the advantages of both deterministic and stochastic simulation. Most of those methods are termed hybrid methods. COPASI also includes several such a hybrid methods which in some systems where deterministic simulation would lead to incorrect results will give the correct time series but is still computationally less demanding than a pure stochastic simulation.