Algorithms
The Gillespie Algorithm
Gillespie's algorithm, also known as the Stochastic Simulation Algorithm, was first described in 1976. It's a popular and, more importantly, exact, dynamic Monte Carlo method, used in the simulation of stochastic systems.
- DT Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22, 403-434 (1976).
- DT Gillespie. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 2340–2361 (1977)
Tau-Leaping
The tau-leaping algorithm is an approximation of Gillespie's algorithm that provides a trade-off between speed and accuracy. Instead of performing one event at a time, the tau-leaping algorithm estimates all of the events that occurred in a given interval of time [t, t+tau), based on the event rates at time t. It can run a great deal faster, but too large a step size can cause significant errors.
- Gillespie, DT. Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics 115, 1716–1711 (2001).
Adaptive Tau-Leaping
Not yet implemented.
- Y Cao, DT Gillespie, and LR Petzold. The adaptive explicit-implicit tau-leaping method with automatic tau selection. Journal of Chemical Physics 126, 224101 (2007).
The Next-Reaction Method
Not yet implemented.
- MA Gibson and J Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry A 104, 1876–1889 (2000).