Y. Komori, D. Cohen and K. Burrage (2015), Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations, Technical Report CSSE-44, Faculty of Computer Science & Systems Engineering, Kyushu Institute of Technology.

Abstract
We propose new explicit exponential Runge-Kutta methods for the weak approximation of solutions of stiff It\^{o} stochastic differential equations (SDEs). These methods have weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term, whereas they are of order two or three for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We perform numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order two.

The material in this report has been superseded by Y. Komori, D. Cohen and K. Burrage (2017).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