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

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 assu...

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Bibliographic Details
Published in:Applied numerical mathematics 2021-04, Vol.162, p.67-80
Main Author: Khan, Feroz
Format: Article
Language:English
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2020.12.011