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The material in this report has been superseded by Y. Komori, D. Cohen and K. Burrage (2017).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.
Last updated: 2017/12/18