Y. Komori, D. Cohen and K. Burrage (2014), High order explicit exponential Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations, Technical Report CSSE-41, Faculty of Computer Science & Systems Engineering, Kyushu Institute of Technology.

Abstract
We are concerned with numerical methods which give weak approximations for stiff Ito stochastic differential equations (SDEs). It is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods when applied to semilinear ODEs. In this paper, we will propose new exponential RK methods which achieve weak order one or two for multi-dimensional, non-commutative SDEs with a semilinear drift term, whereas they are of order one, two or three for semilinear ODEs. We will analytically investigate their stability properties in mean square, and will check their performance in numerical examples.

The material in this report has been superseded by Y. Komori, D. Cohen and K. Burrage (2017).

The pdf file is obtainable from here.

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Last updated: 2017/12/18