Y. Komori and K. Burrage (2023), Split S-ROCK methods for high-dimensional stochastic differential equations, Journal of Scientific Computing, 97 (3), 62.

Abstract
We propose explicit stochastic Runge--Kutta (RK) methods for high-dimensional It\^{o} stochastic differential equations. By providing a linear error analysis and utilizing a Strang splitting-type approach, we construct them on the basis of orthogonal Runge--Kutta--Chebyshev methods of order 2. Our methods are of weak order 2 and have high computational accuracy for relatively large time-step size, as well as good stability properties. In addition, we take stochastic exponential RK methods of weak order 2 as competitors, and deal with implementation issues on Krylov subspace projection techniques for them. We carry out numerical experiments on a variety of linear and nonlinear problems to check the computational performance of the methods. As a result, it is shown that the proposed methods can be very effective on high-dimensional problems whose drift term has eigenvalues lying near the negative real axis and whose diffusion term does not have very large noise.

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Last updated: 2023/10/31