Document Zbl 1247.65006

Küpper, Dominique; Kværnø, Anne; Rößler, Andreas

A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise. (English) Zbl 1247.65006

BIT 52, No. 2, 437-455 (2012).

Summary: The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes are stiffly accurate and applicable to nonlinear stochastic differential-algebraic equations. As an advantage they do not require the calculation of any pseudo-inverses or projectors. Further, the mean-square stability of the proposed schemes is analyzed and simulation results are presented bringing out their good performance.

Cited in 6 Documents

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
34F05	Ordinary differential equations and systems with randomness
34A09	Implicit ordinary differential equations, differential-algebraic equations
65L80	Numerical methods for differential-algebraic equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

stochastic differential-algebraic equation; stochastic Runge-Kutta method; stiffly accurate; mean-square convergence; mean-square stability; numerical examples; Wiener process

Software:

RODAS

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Full Text: DOI

References:

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