Computational and Applied Mathematics seminar

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. 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. This is a joint work with Prof. Kevin Burrage.