Validated Simulation of Differential Algebraic Equations with Runge-Kutta Methods∗†

A Runge-Kutta Method for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise

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 ac...

Projected Runge-kutta Methods for Differential Algebraic Equations of Index 3

In the present paper we introduce a new class of methods, Projected RungeKutta methods, for the solution of index 3 differential algebraic equations (DAEs) in Hessenberg form. The methods admit the integration of index 3 DAEs without any drift effects. This makes them particularly well suited for long term integration. Finally, implemented on the basis of the Radau5 code, the projected Runge-Ku...

Invariant manifolds in differential algebraic equations of index 3 and in their Runge-Kutta discretizations

Implicit Runge–kutta Methods for Transferable Differential-algebraic Equations

The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge–Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is nonsingular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we g...

Asymptotic stability of linear delay differential-algebraic equations and numerical methods *

In this paper, we consider the asymptotic stability of linear constant coefficient delay differential-algebraic equations and of &methods, Runge-Kutta methods and linear multistep methods applied to these systems. o 1997 Published by Elsevier Science B.V.