Numerical analysis of the master equation

Details Numerical analysis of the master equation Numerical analysis of the master equation

2001-10-26

arxiv.org/abs/cond-mat/0110558v1

Phys. Rev. E 65, 047701 (2002)

Physics

Condensed Matter

Statistical Mechanics

7 pages 3 figures

Scientific paper

10.1103/PhysRevE.65.047701

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.

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