Y. Komori (2016), Exponential Runge-Kutta methods for stiff stochastic
differential equations, RIMS Kokyuroku 2005, 128-140.
Abstract
It is well known that the numerical solution of stiff stochastic differential
equations (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 the present paper, such explicit methods
are considered. As a result, the stochastic exponential Euler scheme will
be derived for strong approximations to the solution of stiff It\^{o} SDEs
with a semilinear drift term. In addition, stochastic exponential RK methods
will be derived for weak approximations.
Note
Part of the material in this report has been superseded by Y. Komori and K. Burrage (2014).
The pdf file is obtainable from here.
Last updated: 2017/02/09