Strong first order S-ROCK methods for stochastic differential equations

Authors:
Yoshio Komori;Kevin Burrage
Affiliations:
Department of Systems Design and Informatics, Kyushu Institute of Technology, Iizuka 820-8502, Japan;Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK and Discipline of Mathematics, Queensland University of Technology, Brisbane, QLD 4001, Aust ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

Explicit stochastic Runge-Kutta (SRK) methods are constructed for non-commutative Ito and Stratonovich stochastic differential equations. Our aim is to derive explicit SRK schemes of strong order one, which are derivative free and have large stability regions. In the present paper, this will be achieved by embedding Chebyshev methods for ordinary differential equations in SRK methods proposed by Roszler (2010). In order to check their convergence order, stability properties and computational efficiency, some numerical experiments will be performed.