Towards Automatic Global Error Control: Computable Weak Error Expansion for the Tau-Leap Method
Abstract
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms; a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie algorithm or the Stochastic simulation algorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term.
Cite
@article{arxiv.1004.2948,
title = {Towards Automatic Global Error Control: Computable Weak Error Expansion for the Tau-Leap Method},
author = {Jesper Karlsson and Raul Tempone},
journal= {arXiv preprint arXiv:1004.2948},
year = {2011}
}