Y. Komori, D. Cohen and K. Burrage (2017), Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations, SIAM Journal on Scientific Computing, 39 (6), A2857-A2878.

Abstract
We propose new explicit exponential Runge-Kutta methods for the weak approximation of solutions of stiff It\^{o} stochastic differential equations (SDEs). We also consider the use of exponential Runge-Kutta methods in combination with splitting methods. 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 carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order two.

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Last updated: 2017/12/17