Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

Localization errors in solving stochastic partial differential equations in the whole space


Authors: Máté Gerencsér and István Gyöngy
Journal: Math. Comp. 86 (2017), 2373-2397
MSC (2010): Primary 60H15, 60H35, 65M06
DOI: https://doi.org/10.1090/mcom/3201
Published electronically: November 28, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $ R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. As an application, a numerical scheme is presented which combines the localization and the space and time discretization, and thus is fully implementable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 60H15, 60H35, 65M06

Retrieve articles in all journals with MSC (2010): 60H15, 60H35, 65M06


Additional Information

Máté Gerencsér
Affiliation: School of Mathematics and Maxwell Institute, The University of Edinburgh, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD Scotland, United Kingdom
Address at time of publication: IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
Email: mate.gerencser@ist.ac.at

István Gyöngy
Affiliation: School of Mathematics and Maxwell Institute, The University of Edinburgh, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD Scotland, United Kingdom
Email: gyongy@maths.ed.ac.uk

DOI: https://doi.org/10.1090/mcom/3201
Keywords: Cauchy problem, degenerate stochastic parabolic PDEs, localization error, finite difference method
Received by editor(s): August 22, 2015
Received by editor(s) in revised form: February 27, 2016
Published electronically: November 28, 2016
Article copyright: © Copyright 2016 American Mathematical Society