Convergence analysis of a simplified scheme for stochastic Burgers’ equation with additive noise

Abstract

The aim of this article is to probe the convergence analysis of an efficient scheme, developed by Jentzen et al. (2011), for the stochastic Burgers’ equation (SBE) with term of additive noise. Although, the same scheme was used by Blomker et al. (2013) to carry out the full discretization of the SBE. But therein, Taylor series was not applied. In this work, Taylor series in integral form with remainder after one term is applied. As a consequence, minimum convergence order in time is updated to $3\theta$ from $\theta$, where $\theta \in (0,\frac{1}{2})$. Although, minimum temporal convergence order is proved to be as $2\theta$ by Khan (2021) using the higher order scheme. But the proposed scheme is simple in a manner that former uses two linear functionals of noise, whereas later employs single linear functional of noise. Finally, run time of the existing and the proposed scheme are compared to justify the analytical outcomes.