A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise

作者：Kuepper Dominique; Kvaerno Anne; Roessler Andreas

来源：BIT Numerical Mathematics, 2012, 52(2): 437-455.

DOI：10.1007/s10543-011-0354-0

• Stochastic differential-algebraic equation
• Stochastic Runge-Kutta method
• Stiffly accurate
• Mean-square convergence
• Mean-square stability

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.

• 出版日期2012-6