Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems

Anandaraman Rathinasamy and Priya Nair

Applied Mathematics and Computation, 2018, vol. 332, issue C, 276-303

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.

Keywords: Stochastic differential equations; Multi-dimensional systems; Numerical solutions; Stochastic Runge-–Kutta methods; Mean-square stability analysis; Balanced stochastic Runge–Kutta methods (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:276-303

DOI: 10.1016/j.amc.2018.03.065

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