Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 2003
1193.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and Discretization
, Modelling, Simulation and Optimization of Integrated Circuits: Proceedings of a Conference Held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001Band146, Seite 187
Springer Science \& Business Media
20031192.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, K. and {et al.}, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187--201
Birkhäuser Basel
In Antreich, K. and {et al.}, Editor
Herausgeber: Birkh\"auser Verlag, Basel
20031191.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187–201
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser, Basel
20031190.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187–201
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser, Basel
20031189.
Farkas, Bálint
On the duals of L\sb p spaces with 0<p<1
Acta Math. Hungar., 98 (1-2) :71-77
20031188.
Bátkai, András; Farkas, Bálint
On the effect of small delays to the stability of feedback systems
, Evolution equations: applications to physics, industry, life sciences and economics (<prt>L</prt>evico <prt>T</prt>erme, 2000) Band 55 aus Progr. Nonlinear Differential Equations Appl.
Seite 83-94
Herausgeber: Birkhäuser, Basel
2003
83-941187.
Vogt, Rainer; Scheer, Volker; Casati, Roberto; Benter, Thorsten
On-Road Measurement of Particle Emission in the Exhaust Plume of a Diesel Passenger Car
Environmental Science \& Technology, 37 (18) :4070-4076
20031186.
Vogt, Rainer; Scheer, Volker; Casati, Roberto; Benter, Thorsten
On-Road Measurement of Particle Emission in the Exhaust Plume of a Diesel Passenger Car
Environmental Science \& Technology, 37 (18) :4070-4076
20031185.
Vogt, Rainer; Scheer, Volker; Casati, Roberto; Benter, Thorsten
On-Road Measurement of Particle Emission in the Exhaust Plume of a Diesel Passenger Car
Environmental Science & Technology, 37 (18) :4070-4076
20031184.
Maten, E. J. W.; Fijnvandraat, J. G.; Lin, C.; Peters, J. M. F.
Periodic {AC} and Periodic Noise in {RF} Simulation for Electronic Circuit Design
In K. Antreich and R. Bulirsch and A. Gilg and P. Rentrop, Editor, Modeling, Simulation, and Optimization of Integrated Circuits Band 146 aus Int. Series of Numer. Maths.
Seite 121--134
Herausgeber: Birkhäuser Basel
2003
121--1341183.
Farkas, Bálint
Perturbations of Bi-Continuous Semigroups
Eötvös Loránd University
20031182.
[english] Bohrmann-Linde, Claudia; Tausch, Michael W.
Photogalvanic Cells for Classroom Investigations: A Contribution for Ongoing Curriculum Modernization
Journal of Chemical Education, 80 (12) :1471
2003
Herausgeber: American Chemical Society ({ACS})1181.
Farkas, Bálint; Matolcsi, Máté
Positive forms on Banach spaces
Acta Math. Hungar., 99 (1-2) :43-55
20031180.
Yurchenko, Sergey N.; Carvajal, Miguel; Jensen, Per; Herregodts, F.; Huet, T. R.
Potential parameters of PH\(_{3}\) obtained by simultaneous fitting of ab initio data and experimental vibrational band origins
Chemical Physics, 290 (1) :59-67
2003
Herausgeber: North-Holland1179.
Yurchenko, Sergey N.; Carvajal, Miguel; Jensen, Per; Herregodts, F.; Huet, T. R.
Potential parameters of PH\(_{3}\) obtained by simultaneous fitting of ab initio data and experimental vibrational band origins
Chemical Physics, 290 (1) :59-67
2003
Herausgeber: North-Holland1178.
Yurchenko, Sergey N.; Carvajal, Miguel; Jensen, Per; Herregodts, F.; Huet, T. R.
Potential parameters of PH3 obtained by simultaneous fitting of ab initio data and experimental vibrational band origins
Chemical Physics, 290 (1) :59-67
2003
Herausgeber: North-Holland1177.
Günther, Michael; Arnold, Martin
Preconditioned splitting and overlapping techniques in modular time integration
4th MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingausArgesim Report 24, Seite 1382–1387
Herausgeber: TU Wien
20031176.
G\"unther, Michael; Arnold, M.
Preconditioned splitting and overlapping techniques in modular time integration
Mathmod 4 Proceedings
20031175.
Günther, Michael; Arnold, Martin
Preconditioned splitting and overlapping techniques in modular time integration
4th MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingausArgesim Report 24, Seite 1382–1387
Herausgeber: TU Wien
20031174.
Jankova, Katja; Hvilsted, S{\o}ren
Preparation of Poly(2,3,4,5,6-pentafluorostyrene) and Block Copolymers with Styrene by ATRP
Macromolecules, 36 (5) :1753--1758
2003
ISSN: 0024-92971173.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Pr{é}v{{\^o}}t, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031172.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Pr{é}v{{\^o}}t, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031171.
Sturm, Peter J.; Baltensperger, Urs; Bacher, Michael; Lechner, Bernhard; Hausberger, Stefan; Heiden, Bernhard; Imhof, David; Weingartner, Ernest; Prévôt, Andre S. H.; Kurtenbach, Ralf; Wiesen, Peter
Roadside measurements of particulate matter size distribution
, Atmospheric EnvironmentBand37, Seite 5273-5281
Herausgeber: Pergamon
20031170.
Heilmann, Margareta
Rodriguez-type representation for the eigenfunctions of Durrmeyer-type operators
Results in Mathematics, 44 (1-2) :97-105
20031169.
Lamour, R.; März, R.; Winkler, R.
Stability of periodic solutions of index-2 differential-algebraic systems
J. Math. Anal. Appl., 279 :475--494
2003
