title: Stochastic linear multistep methods for the simulation of chemical kinetics.
abstract: In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the τ-leaping framework to past information. Using the Θ-trapezoidal τ-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k ≥ 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.
authors: Departamento de Informática, University of Valladolid, Valladolid, Spain.
authors: Manuel
authors: M
authors: Barrio
authors: Department of Computer Science, University of Oxford, Oxford, United Kingdom.
authors: Kevin
authors: K
authors: Burrage
authors: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
authors: Pamela
authors: P
authors: Burrage
mesh_terms: D066246:ErbB Receptors / Q000737:chemistry; D007700:Kinetics; D016014:Linear Models; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes
chemical_list: D066246:ErbB Receptors