Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

Burrage, Kevin & Burrage, Pamela (2012) Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise. Journal of Computational and Applied Mathematics, 236(16), pp. 3920-3930.

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In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

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ID Code: 50974
Item Type: Journal Article
Refereed: Yes
Keywords: stochastic Hamiltonian problems, Runge-Kutta methods, symplecticity
DOI: 10.1016/j.cam.2012.03.007
ISSN: 0377-0427
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier B.V.
Copyright Statement: NOTICE: this is the authors' version of a work that was accepted for publication in the Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, Volume 236, Issue 16, October 2012, Pages 3920–3930.
Deposited On: 20 Jun 2012 03:59
Last Modified: 02 Nov 2013 08:22

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