Weak second order S-ROCK methods for Stratonovich 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:
2012

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Abstract

It is well known that the numerical solution of stiff stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit or semi-implicit methods with a wide variety of stability properties. However, for stiff stochastic problems in which the eigenvalues of a drift term lie near the negative real axis, such as those arising from stochastic partial differential equations, explicit methods with extended stability regions can be very effective. In the present paper our aim is to derive explicit Runge-Kutta schemes for non-commutative Stratonovich stochastic differential equations, which are of weak order two and which have large stability regions. This will be achieved by the use of a technique in Chebyshev methods for ordinary differential equations.