Burrage, K and Lythe, G orcid.org/0000-0001-7966-5571 (2014) Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations. Stochastic Partial Differential Equations: Analysis and Computations, 2 (2). pp. 262-280. ISSN 2194-0401
Abstract
We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014, Springer Verlag. This is an author produced version of a paper published in Stochastic Partial Differential Equations: Analysis and Computations. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via http://dx.doi.org/10.1007/s40072-014-0032-8 |
Keywords: | Stationary density; Stochastic Runge–Kutta methods; Leapfrog methods; Correlation function |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EU - European Union 317040 BBSRC BB/F003811/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 May 2017 15:03 |
Last Modified: | 20 Jan 2018 13:24 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s40072-014-0032-8 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109678 |