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The problem of solving stochastic differential-algebraic equations (SDAEs) ofindex one with a scalar driving Brownian motion is considered. Recently, theauthors proposed a class of stiffly accurate stochastic Runge-Kutta (SRK)methods that do not involve any pseudo-inverses or projectors for the numericalsolution of the problem. Based on this class of approximation methods, aclassification for the coefficients of stiffly accurate SRK methods attainingstrong order 0.5 as well as strong order 1.0 are calculated. Further, themean-square stability for the considered class of SRK methods is analysed. Asthe main result, families of A-stable efficient order 0.5 and 1.0 stifflyaccurate SRK methods with a minimal number of stages for SDEs as well as forSDAEs are presented.

Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise