Applied and Computational Mathematics (ACM)

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

1188.

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
83-94

1187.

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
2003

DOI: 10.1021/es0300315

1186.

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
2003

DOI: 10.1021/es0300315

1185.

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
2003

DOI: 10.1021/es0300315

1184.

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--134

DOI: 10.1007/978-3-0348-8065-7_8

1183.

Farkas, Bálint
Perturbations of Bi-Continuous Semigroups
Eötvös Loránd University
2003

1182.

[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})

DOI: 10.1021/ed080p1471

1181.

Farkas, Bálint; Matolcsi, Máté
Positive forms on Banach spaces
Acta Math. Hungar., 99 (1-2) :43-55
2003

1180.

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-Holland

DOI: 10.1016/S0301-0104(03)00098-3

1179.

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-Holland

DOI: 10.1016/S0301-0104(03)00098-3

1178.

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-Holland

DOI: 10.1016/S0301-0104(03)00098-3

1177.

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
2003

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1176.

G\"unther, Michael; Arnold, M.
Preconditioned splitting and overlapping techniques in modular time integration
Mathmod 4 Proceedings
2003

1175.

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
2003

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1174.

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: 0024-9297

DOI: 10.1021/ma021039m

1173.

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
2003

DOI: 10.1016/j.atmosenv.2003.05.006

1172.

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
2003

DOI: 10.1016/j.atmosenv.2003.05.006

1171.

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
2003

DOI: 10.1016/j.atmosenv.2003.05.006

1170.

Heilmann, Margareta
Rodriguez-type representation for the eigenfunctions of Durrmeyer-type operators
Results in Mathematics, 44 (1-2) :97-105
2003

DOI: 10.1007/BF03322916

1169.

Lamour, R.; März, R.; Winkler, R.
Stability of periodic solutions of index-2 differential-algebraic systems
J. Math. Anal. Appl., 279 :475--494
2003

1168.

Kirsch, Stefan; Bach, Thorsten
Stereoselective Synthesis of Enantiomerically Pure, Orthogonally Protected 2-Methylenecyclohexane-1,3,5-triols and 2,4,6-Trihydroxycyclohexanones
Synthesis, 2003 (12) :1827–1836
2003
ISSN: 0039-7881, 1437-210X

DOI: 10.1055/s-2003-41025

1167.

Römisch, W.; Winkler, R.
Stochastic {DAEs} in circuit simulation
In Antreich, K. and Bulirsch, R. and Gilg, A. and Rentrop, P., Editor, Modeling, Simulation and Optimization of Integrated Circuits, Seite 303--318
In Antreich, K. and Bulirsch, R. and Gilg, A. and Rentrop, P., Editor
Herausgeber: Birkhäuser, Basel
2003

1166.

Winkler, R.
Stochastic Differential Algebraic Equations of Index 1 and Applications in Circuit Simulation
J. Comp. Math. Appl., 157 :477--505
2003

1165.

Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
STOFF-FORMEL-UMWELT, Chemie für Schjg. 8 in Niedersachsen
Herausgeber: C. C. Buchner, Bamberg
2003

1164.

Setzer, Klaus-Dieter; Kalb, M.; Fink, Ewald H.
The a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) magnetic dipole transition of S\(_{2}\)
Journal of Molecular Spectroscopy, 221 (1) :127-130
2003
Herausgeber: Academic Press

DOI: 10.1016/S0022-2852(03)00174-7