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

2013/11/04 by Dominique Küpper, Küpper, Dominique, Anne Kværnø +3 · 2 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H35 #65C30 #65L20 #65L80 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1311.0809

openalex publication_date 2013/11/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

The problem of solving stochastic differential-algebraic equations (SDAEs) of\nindex one with a scalar driving Brownian motion is considered. Recently, the\nauthors proposed a class of stiffly accurate stochastic Runge-Kutta (SRK)\nmethods that do not involve any pseudo-inverses or projectors for the numerical\nsolution of the problem. Based on this class of approximation methods, a\nclassification for the coefficients of stiffly accurate SRK methods attaining\nstrong order 0.5 as well as strong order 1.0 are calculated. Further, the\nmean-square stability for the considered class of SRK methods is analysed. As\nthe main result, families of A-stable efficient order 0.5 and 1.0 stiffly\naccurate SRK methods with a minimal number of stages for SDEs as well as for\nSDAEs are presented.\n

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