Weak first- or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process

Authors:
Yoshio Komori
Affiliations:
Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Iizuka 820-8502, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

New fully implicit stochastic Runge-Kutta schemes of weak order 1 or 2 are proposed for stochastic differential equations with sufficiently smooth drift and diffusion coefficients and a scalar Wiener process, which are derivative-free and which are A-stable in mean square for a linear test equation in some general settings. They are sought in a transparent way and their convergence order and stability properties are confirmed in numerical experiments.