Article ID Journal Published Year Pages File Type
8900946 Applied Mathematics and Computation 2018 28 Pages PDF
Abstract
In this paper, the linear asymptotic mean-square stability of the weak second-order stochastic Runge-Kutta methods for multi-dimensional Itô stochastic differential equations due to Rößler (2009) and Tang and Xiao (2017) are obtained. Further, we have developed the stochastic Runge-Kutta methods for multi-dimensional Itô stochastic differential equations to the balanced stochastic Runge-Kutta methods by using the control functions. We carry out a linear stability analysis of the class of stochastic Runge-Kutta methods for the linear test equations with multiplicative noise thereby providing an explicit structure of stability matrices. Some comparisons and illustrations shows that there is an improvement in the stability and error analysis of these new balanced stochastic Runge-Kutta methods comparatively to stochastic Runge-Kutta methods and thus conforming the obtained theoretical results.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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