Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise
Abstract
The problem of solving stochastic differential-algebraic equations (SDAEs) of index one with a scalar driving Brownian motion is considered. Recently, the authors proposed a class of stiffly accurate stochastic Runge-Kutta (SRK) methods that do not involve any pseudo-inverses or projectors for the numerical solution of the problem. Based on this class of approximation methods, a classification for the coefficients of stiffly accurate SRK methods attaining strong order 0.5 as well as strong order 1.0 are calculated. Further, the mean-square stability for the considered class of SRK methods is analysed. As the main result, families of A-stable efficient order 0.5 and 1.0 stiffly accurate SRK methods with a minimal number of stages for SDEs as well as for SDAEs are presented.
Keywords
Cite
@article{arxiv.1311.0809,
title = {Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise},
author = {Dominique Küpper and Anne Kværnø and Andreas Rößler},
journal= {arXiv preprint arXiv:1311.0809},
year = {2013}
}