Stability analysis and classification of Runge–Kutta methods for index 1 stochastic differential-algebraic equations with scalar noise

• Published in: Applied numerical mathematics Vol. 96; pp. 24 - 44
• Main Authors: Kuepper, Dominique, Kvaernoe, Anne, Rosler, Andreas
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2015
• Subjects: A-stability; Approximation; Classification; Mathematical analysis; Mathematical models; Mean-square stability; Projectors; Runge-Kutta method; Scalars; Stochastic differential-algebraic equation; Stochastic Runge–Kutta method; Stochasticity; Stochastic Runge–Kutta method; Mean-square stability; Classification; Stochastic differential-algebraic equation; A-stability
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2015.04.003

The problem of solving stochastic differential-algebraic equations (SDAEs) of index 1 with a scalar driving Wiener process is considered. Recently, the authors have 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, classifications 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 of the considered class of SRK methods is analyzed. 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.