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



1999

803.

Bunker, Philip R.; Bludsk{{\'y}}, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H\(_{2}\)O\(^{++}\) Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999

802.

Bunker, Philip R.; Bludský, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H2O++ Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999

801.

Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999

800.

Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999

799.

Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999

798.

Gänsheimer, S; Schilling, A
Verbesserte prätherapeutische Abschätzung des pathologischen Tumorstadiums des Prostatakarzinoms anhand eines neuen Punktsystems
Aktuelle Urologie, 30 (01) :20--27
1999
Herausgeber: Georg Thieme Verlag Stuttgart{\textperiodcentered} New York

797.

[german] Tausch, Michael W.; Schmidt, Andrea
β-Carotin - ein Multitalent
CHEMKON, 6 (3) :135--141
1999
Herausgeber: Wiley
1998

796.

Tausch, Michael W.; Lowin, P.; Übel, M.
''Materialien-Manager Chemie'' Multimedia CD-ROM zur Erstellung von Arbeitsmaterialien für den Chemieunterricht
Herausgeber: C. C. Buchner, Bamberg
1998

795.

Tausch, Michael W.; Wachtendonk, M.; Porth, H.-R.; Schulze, I.; Wambach, H.
''STOFF-FORMEL-UMWELT'', CHEMIE S I, 7. Schjg. in NRW
Herausgeber: C. C. Buchner, Bamberg
1998

794.

Jacob, Birgit
A formula for the stability radius of time-varying systems
J. Differential Equations, 142 (1) :167--187
1998

793.

Feldmann, Uwe
CAD-based electric-circuit modeling in industry II: Impact of circuit configurations and parameters
Surveys on Mathematics for Industry, 8 (2) :131--158
1998
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.

792.

Jacob, Birgit; Larsen, Mikael; Zwart, Hans
Corrections and extensions of: ``Optimal control of linear systems with almost periodic inputs" [SIAM J. Control Optim. \bf 25 (1987), no. 4, 1007--1019; MR0893995 (88i:93042)] by G. Da Prato and A. Ichikawa
SIAM J. Control Optim., 36 (4) :1473--1480
1998

791.

[german] Tausch, Michael W.; Balzer, M.
Die Ketone und das Licht
Praxis der Naturwissenschaften (Chemie), 47 (7) :14
1998

790.

Ehrhardt, Matthias
Discrete transparent boundary conditions for wide angle parabolic equations in underwater
Journal of Computational Physics, 145 :469--470
1998

789.

Ehrhardt, Matthias
Discrete Transparent Boundary Conditions For Wide Angle Parabolic Equations In Underwater Acoustics
Journal of Computational Physics, 145 :469-470
1998

788.

Ehrhardt, Matthias
Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics
Journal of Computational Physics, 145 (2) :611–638
1998
Herausgeber: Elsevier

787.

Tausch, Michael W.; Grolmuss, A.; Piwek, B.
Echtfarben-Emissionsspektren EFES - Ein Beitrag zum Verständnis von Licht und Farbe
Praxis der Naturwissenschaften (Chemie), 47 (2) :10
1998

786.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

785.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

784.

Shestakov, Oleg; Breidohr, R.; Demes, H.; Setzer, Klaus-Dieter; Fink, Ewald H.
Electronic States and Spectra of BiO
Journal of Molecular Spectroscopy, 190 (1) :28-77
1998
Herausgeber: Academic Press

783.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

782.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

781.

Brasseur, G. P.; Cox, R. A.; Hauglustaine, D.; Isaksen, I.; Lelieveld, J.; Lister, D. H.; Sausen, R.; Schumann, Ulrich; Wahner, A.; Wiesen, Peter
European scientific assessment of the atmospheric effects of aircraft emissions
Atmospheric Environment, 32 (13) :2329-2418
1998

780.

Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press

779.

Shestakov, Oleg; Gielen, R.; Setzer, Klaus-Dieter; Fink, Ewald H.
Gas phase LIF study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) ↔ X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\),X\(_{2}\)1) transition of NI
Journal of Molecular Spectroscopy, 192 (1) :139-147
1998
Herausgeber: Academic Press