Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

Burrage, Pamela & Burrage, Kevin (2014) Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise. Numerical Algorithms, 65(3), pp. 519-532.

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Abstract

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.

Impact and interest:

3 citations in Scopus
3 citations in Web of Science®
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ID Code: 64187
Item Type: Journal Article
Refereed: Yes
Keywords: stochastic Hamiltonian problems, Runge-Kutta methods, symplecticity
DOI: 10.1007/s11075-013-9796-6
ISSN: 1017-1398
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Springer
Deposited On: 05 May 2014 22:54
Last Modified: 07 May 2014 08:05

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