Higher order pathwise approximation for the stochastic Burgers' equation with additive noise

Abstract

This article aims to investigate the pathwise convergence of the higher order scheme, introduced by Jentzen (2011) [9], for the stochastic Burgers' equation (SBE) driven by space-time white noise. In particular, first and second order derivatives of the non-linear drift term of the SBE are assumed to be defined and bounded in Sobolev spaces using the definition of distribution derivative i.e. Lemma 4.7 in Blömker and Jentzen (2013) [2] is extended. Based on this extension, temporal convergence analysis of the higher order scheme is carried out for the SBE with additive noise. As a result, minimum temporal convergence order is improved from θ (Theorem 4.1 in Blömker et al. (2013) [3]) to 2θ, where every θ∈(0,12)). Numerical experiments are performed to validate the theoretical findings.