Stability preserving integration of index-2 DAEs

Authors:
I. Higueras;R. März;C. Tischendorf
Affiliations:
Universidad Pública de Navarra, Departamento de Matemática e Informática, 31006 Pamplona, Spain;Humboldt University of Berlin, Institute of Mathematics, 10099 Berlin, Germany;Humboldt University of Berlin, Institute of Mathematics, 10099 Berlin, Germany
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 6
Cited 7

Stability of computational methods for constrained dynamics systems

SIAM Journal on Scientific Computing
On Asymptotics in Case of Linear Index-2 Differential-Algebraic Equations

SIAM Journal on Numerical Analysis
Runge-Kutta methods for DAEs. A new approach

Proceedings of the on Numerical methods for differential equations
Analyzing the stability behaviour of solutions and their approximations in case of index-2 differential-algebraic systems

Mathematics of Computation
Differential algebraic systems anew

Applied Numerical Mathematics
Stability preserving integration of index-1 DAEs

Applied Numerical Mathematics

Adjoint pairs of differential-algebraic equations and Hamiltonian systems

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Error analysis of Parallel Multivalue Hybrid Methods for index-2 Differential-Algebraic Equations

International Journal of Computing Science and Mathematics
The properties of differential-algebraic equations representing optimal control problems

Applied Numerical Mathematics
Adjoint pairs of differential-algebraic equations and Hamiltonian systems

Applied Numerical Mathematics
Differential algebraic equations with properly stated leading terms

Computers & Mathematics with Applications
Jacobi spectral solution for integral algebraic equations of index-2

Applied Numerical Mathematics
Structural analysis of electrical circuits including magnetoquasistatic devices

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

For linear index-2 DAEs with properly stated leading term we characterize contractive and dissipative flows. We study under which conditions the qualitative properties of the DAE solutions are reflected by the numerical approximations. This is the case if the discretization and the decoupling processes commute. Commutativity is achieved if two subspaces associated with the index-2 DAE are constant; in this case we say that the index-2 DAE is numerically qualified. If both subspaces are time dependent, the problem should be reformulated; in order to avoid numerically equivalent reformulations, a criterion is given. If only one of these subspaces is constant, the problem is in some sense close to a numerically qualified one and thus depending on the problem context, no reformulations are needed. Contractive and dissipative flows induced by the DAE are characterized and results on qualitative properties of the numerical solution are given.