A Computable Weak Error Expansion for the Tau-Leap Method

In this talk I will present an a posteriori error expansion with computable leading order term for the global weak error in the tau-leap approximation 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 as well as 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. I will here also present a comparison between
the work for the two methods depending on the propensity regime, based on an a priori estimate for the relative global weak error.