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

2002

1114.

Dearing, P.M.; Hamacher, Horst W.; Klamroth, Kathrin
Dominating sets for rectilinear center location problems with polyhedral barriers
Naval Research Logistics, 49 :647-665
2002

DOI: 10.1002/nav.10038

1113.

Ehrhardt, M.
Efficient Numerical Implementation of Discrete Transparent Boundary Conditions for Parabolic Equations
Proceedings of the Sixth European Conference on Underwater Acoustics, June 24-27, 2002, Gdansk, Poland, Seite 381--386
2002

1112.

Ehrhardt, Matthias
Efficient numerical implementation of discrete transparent boundary conditions for parabolic equations in underwater acoustics
Acta Acustica united with Acustica, 88 (5) :711--713
2002
Herausgeber: S. Hirzel Verlag

1111.

Ehrhardt, Matthias
Efficient numerical implementation of discrete transparent boundary conditions for parabolic equations in underwater acoustics
Acta Acustica united with Acustica, 88 (5) :711–713
2002
Herausgeber: S. Hirzel Verlag GmbH

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1110.

Tausch, Michael W.; Bohrmann, Claudia; Seesing, Michael
Eine no-cost Brennstoffzelle
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (6)
2002

1109.

[german] Bohrmann, Claudia; Tausch, Michael W.
Elektrochemolumineszenz mit unbedenklichen Chemikalien: Das leuchtende Scherblatt
Chemie in unserer Zeit, 36 (3) :164--167
2002
Herausgeber: Wiley

DOI: 10.1002/1521-3781(200206)36:3<164::aid-ciuz164>3.0.co;2-j

1108.

Tausch, Michael W.; Korn, S.
Experimentelle Schulchemie
In W. Gl{\"o}ckner and W. Jansen, Editor
Kapitel Modellversuche zum Zyklus Photosynthese-Atmung, Seite 8
Herausgeber: Aulis, K{\"o}ln
2002
8

1107.

Winkler, J.; Blank, P.; Glaser, K.; Gomes, J. A. G.; Habram, M.; Jambert, C.; Jaeschke, W.; Konrad, S.; Kurtenbach, Ralf; Lenschow, P.; L{ö}rzer, Jutta C.; Perros, P. E.; Pesch, M.; Pr{ü}mke, H. J.; Rappengl{ü}ck, Bernhard; Schmitz, Th.; Slemr, F.; Volz-Thomas, A.; Wickert, B.
Ground-based and airborne measurements of nonmethane hydrocarbons in BERLIOZ: Analysis and selected results
Journal of Atmospheric Chemistry, 42 (1-3) :465-492
2002

DOI: 10.1023/A:1015709214016

1106.

Winkler, J.; Blank, P.; Glaser, K.; Gomes, J. A. G.; Habram, M.; Jambert, C.; Jaeschke, W.; Konrad, S.; Kurtenbach, Ralf; Lenschow, P.; Lörzer, Jutta C.; Perros, P. E.; Pesch, M.; Prümke, H. J.; Rappenglück, Bernhard; Schmitz, Th.; Slemr, F.; Volz-Thomas, A.; Wickert, B.
Ground-based and airborne measurements of nonmethane hydrocarbons in BERLIOZ: Analysis and selected results
Journal of Atmospheric Chemistry, 42 (1-3) :465-492
2002

DOI: 10.1023/A:1015709214016

1105.

Winkler, J.; Blank, P.; Glaser, K.; Gomes, J. A. G.; Habram, M.; Jambert, C.; Jaeschke, W.; Konrad, S.; Kurtenbach, Ralf; Lenschow, P.; L{ö}rzer, Jutta C.; Perros, P. E.; Pesch, M.; Pr{ü}mke, H. J.; Rappengl{ü}ck, Bernhard; Schmitz, Th.; Slemr, F.; Volz-Thomas, A.; Wickert, B.
Ground-based and airborne measurements of nonmethane hydrocarbons in BERLIOZ: Analysis and selected results
Journal of Atmospheric Chemistry, 42 (1-3) :465-492
2002

DOI: 10.1023/A:1015709214016

1104.

Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~=\(^{2}\)A' → X\verb=~=\(^{2}\)A'' transition of DO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 216 (2) :322-334
2002
Herausgeber: Academic Press

DOI: 10.1006/jmsp.2002.8621

1103.

Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~=\(^{2}\)A' → X\verb=~=\(^{2}\)A'' transition of DO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 216 (2) :322-334
2002
Herausgeber: Academic Press

DOI: 10.1006/jmsp.2002.8621

1102.

Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A~2A' → X~2A" transition of DO2: Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 216 (2) :322-334
2002
Herausgeber: Academic Press

DOI: 10.1006/jmsp.2002.8621

1101.

Tausch, Michael W.; Wachtendonk, M.
Induktiv zu den Molekülen - ein Unterrichtsbaustein zur Einführung des Molekülbegriffs
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (6) :8
2002

1100.

Schandl, Bernd; Klamroth, Kathrin; Wiecek, Margaret M.
Introducing oblique norms into multiple criteria programming
Journal of Global Optimization, 23 :81-97
2002

DOI: 10.1023/A:1014021806919

1099.

Bohrmann-Linde, Claudia
Labothek Duisburg
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (8)
2002

1098.

Tausch, Michael W.; Wachtendonk, M.; Buric, R.; Krollmann, P.; Schmitz, W.; Schulze, I.; Wambach, H.
Lehrerband zu CHEMIE 2000+, Lehrbuch für die gymnasiale Oberstufe, Band 1
Herausgeber: C. C. Buchner, Bamberg
2002

1097.

Bartel, Andreas; Günther, Michael; Kværnø, Anne
Multirate methods in electrical circuit simulation
In Anile, Angelo Marcello and Capasso, Vincenzo and Greco, Antonio, Editor, Progress in Industrial Mathematics at ECMI 2000ausMathematics in Industry, Seite 258–265
In Anile, Angelo Marcello and Capasso, Vincenzo and Greco, Antonio, Editor
Herausgeber: Springer Berlin Heidelberg
2002

DOI: 10.1007/978-3-662-04784-2_35

1096.

Bartel, Andreas; Günther, Michael; Kværnø, Anne
Multirate methods in electrical circuit simulation
In A.M. Anile and V. Capasso and A. Greco, Editor, Progress in Industrial Mathematics at ECMI 2000ausMathematics in Industry 1, Seite 258--265
Springer Berlin Heidelberg
In A.M. Anile and V. Capasso and A. Greco, Editor
Herausgeber: Springer-Verlag, Berlin
2002

1095.

Klar, A; Materne, T; Wegener, R
Multivalued fundamental diagrams and stop and go waves for continuum traffic equations
2002

1094.

Schandl, Bernd; Klamroth, Kathrin; Wiecek, Margaret M.
Norm-Based Approximation in Multicriteria Programming
Computers and Mathematics with Applications, 44 :925-942
2002

DOI: 10.1016/S0898-1221(02)00204-3

1093.

Bartel, Andreas; Günther, Michael; Pulch, Roland; Rentrop, Peter
Numerical techniques for different time scales in electric circuit simulation
In Breuer, Michael and Durst, Franz and Zenger, Christoph, Editor, High Performance Scientific and Engineering ComputingBand21ausLecture Notes in Computational Science and Engineering, Seite 343–360
In Breuer, Michael and Durst, Franz and Zenger, Christoph, Editor
Herausgeber: Springer Berlin Heidelberg
2002

DOI: 10.1007/978-3-642-55919-8_38

1092.

Bartel, A; Pulch, R; Rentrop, P
Numerical techniques for different time scales in electric circuit simulation
In M. Breuer and F. Durst and Chr. Zenger, Editor, High Performance Scientific And Engineering Computing: Proceedings of the 3rd International FORTWIHR Conference on HPSEC, Erlangen, March 12--14, 2001Band21ausLecture Notes in Computational Science and Engineering, Seite 343--360
Springer Berlin Heidelberg
In M. Breuer and F. Durst and Chr. Zenger, Editor
2002

1091.

Tausch, Michael W.; Knauf, U.
Online-Materialien zum Thema Ozon, Hypermedia-Netzwerk mit Experimenten, Arbeitsblättern, Folien, Videos, Links etc.
Online ( www.lehrer-online.de )
2002

1090.

Tausch, Michael W.
PISA - für Insider nicht viel Neues
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (6) :11
2002