SIAM Journal on Algebraic and Discrete Methods
Runge-Kutta methods for DAEs. A new approach
Proceedings of the on Numerical methods for differential equations
Stability preserving integration of index-1 DAEs
Applied Numerical Mathematics
Stability preserving integration of index-2 DAEs
Applied Numerical Mathematics
Singularity crossing phenomena in DAEs: A two-phase fluid flow application case study
Computers & Mathematics with Applications
Characterizing differential algebraic equationswithout the use of derivative arrays
Computers & Mathematics with Applications
Applied Numerical Mathematics
Self-heating in a coupled thermo-electric circuit-device model
Journal of Computational Electronics
A new algorithm for index determination in DAEs using algorithmic differentiation
Numerical Algorithms
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In this paper, we study differential algebraic equations (DAEs) of the form A(@g, t)(d(@g, t))'+ b(@g, t) = 0 with in some sense well-matched matrix functions A(@g, t) and D(@g, t) := d'"@g (@g, t) as they arise, e.g., in circuit simulation. We characterize index 1 DAEs in this context. After analyzing those index 1 equations themselves, we apply Runge-Kutta methods and BDFs, provide stability inequalities, and show convergence. The cases of the image space of D(@g, t) or the nullspace of A(@g, t) remaining constant are pointed out to be essentially favourable for the qualitative behaviour of the approximations on long intervals. Hence, when modelling with DAEs one should try for those, constant subspaces. Relations to quasilinear DAEs in standard formulation E(@g, t)@g' + @? (@g, t) = 0 are considered, too.