Technical Report Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations

Komori, Yoshio  ,  Cohen, David  ,  Burrage, Kevin

Description
We propose new explicit exponential Runge-Kutta methods for the weak approximation of solutions of stiff Ito stochastic differential equations (SDEs). These methods have weak order two for multi-dimensional, non-commutative SDEs with a semi- linear 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.
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