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: 882.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Buenker, Robert J.; Gu, Jian-ping; Hirsch, Gerhard
A Theoretical Investigation of the Renner Interactions and Magnetic Dipole Transitions in the A\verb=~=-X\verb=~= Electronic Band System of HO\(_{2}\)
Journal of Molecular Spectroscopy, 197 (2) :262-274
1999
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1999.7919; 881.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Buenker, Robert J.; Gu, Jian-ping; Hirsch, Gerhard
A Theoretical Investigation of the Renner Interactions and Magnetic Dipole Transitions in the A~-X~ Electronic Band System of HO2
Journal of Molecular Spectroscopy, 197 (2) :262-274
1999
Herausgeber: Academic Press
DOI: 10.1006/JMSP.1999.7919; 880.
Benter, Thorsten; Appel, Matthew F.; Garnica, R. M.; Schmidt, Sven; Schindler, Ralph N.
Atmospheric pressure laser ionization mass spectrometry (APLI MS): Potential analytical applications in medical diagnostics and environmental chemistry.
Abstracts of Papers of The Americal Chemical Society, 218 (1) :U174-U175
1999; 879.
Benter, Thorsten; Appel, Matthew F.; Garnica, R. M.; Schmidt, Sven; Schindler, Ralph N.
Atmospheric pressure laser ionization mass spectrometry (APLI MS): Potential analytical applications in medical diagnostics and environmental chemistry.
Abstracts of Papers of The Americal Chemical Society, 218 (1) :U174-U175
1999; 878.
Benter, Thorsten; Appel, Matthew F.; Garnica, R. M.; Schmidt, Sven; Schindler, Ralph N.
Atmospheric pressure laser ionization mass spectrometry (APLI MS): Potential analytical applications in medical diagnostics and environmental chemistry.
Abstracts of Papers of The Americal Chemical Society, 218 (1) :U174-U175
1999; 877.
Schmidt, Sven; Appel, Matthew F.; Garnica, R. M.; Schindler, Ralph N.; Benter, Thorsten
Atmospheric Pressure Laser Ionization. An Analytical Technique for Highly Selective Detection of Ultralow Concentrations in the Gas Phase
Analytical Chemistry, 71 (17) :3721-3729
1999
DOI: 10.1021/ac9901900; 876.
Schmidt, Sven; Appel, Matthew F.; Garnica, R. M.; Schindler, Ralph N.; Benter, Thorsten
Atmospheric Pressure Laser Ionization. An Analytical Technique for Highly Selective Detection of Ultralow Concentrations in the Gas Phase
Analytical Chemistry, 71 (17) :3721-3729
1999
DOI: 10.1021/ac9901900; 875.
Schmidt, Sven; Appel, Matthew F.; Garnica, R. M.; Schindler, Ralph N.; Benter, Thorsten
Atmospheric Pressure Laser Ionization. An Analytical Technique for Highly Selective Detection of Ultralow Concentrations in the Gas Phase
Analytical Chemistry, 71 (17) :3721-3729
1999
DOI: 10.1021/ac9901900; 874.
Günther, M.; Feldmann, U.
CAD-based electric circuit modeling in industry I: mathematical structure and index of network equations
Surveys on Mathematics for Industry, 8 :97–129
1999
Herausgeber: Springer
Download; 873.
Günther, M.; Feldmann, U.
CAD-based electric circuit modeling in industry II: impact of circuit configurations and parameters
Surveys on Mathematics for Industry, 8 :131–157
1999
Herausgeber: Springer
Download; 872.
Caldwell, Tracy E.; Foster, Krishna L.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Characterization of HOCl Using Atmospheric Pressure Ionization Mass Spectrometry
The Journal of Physical Chemistry A, 103 (41) :8231-8238
1999
DOI: 10.1021/jp9906841; 871.
Caldwell, Tracy E.; Foster, Krishna L.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Characterization of HOCl Using Atmospheric Pressure Ionization Mass Spectrometry
The Journal of Physical Chemistry A, 103 (41) :8231-8238
1999
DOI: 10.1021/jp9906841; 870.
Caldwell, Tracy E.; Foster, Krishna L.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Characterization of HOCl Using Atmospheric Pressure Ionization Mass Spectrometry
The Journal of Physical Chemistry A, 103 (41) :8231-8238
1999
DOI: 10.1021/jp9906841; 869.
Jacob, Birgit; Winkin, Joseph; Zwart, Hans
Continuity of the spectral factorization on a vertical strip
Systems Control Lett., 37 (4) :183--192
1999
DOI: 10.1016/S0167-6911(99)00019-5; 868.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging and the CH\(_{2}\)\(^{+}\) molecule
Chemical Physics Letters, 309 (3-4) :299-306
1999
DOI: 10.1016/S0009-2614(99)00682-X; 867.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging and the CH\(_{2}\)\(^{+}\) molecule
Chemical Physics Letters, 309 (3-4) :299-306
1999
DOI: 10.1016/S0009-2614(99)00682-X; 866.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging and the CH2+ molecule
Chemical Physics Letters, 309 (3-4) :299-306
1999
DOI: 10.1016/S0009-2614(99)00682-X; 865.
Korn, Silke; Eisel, Christian; Tausch, Michael W.
Das leuchtende Labor
{CHEMKON}, 6 (3) :142--142
1999
Herausgeber: Wiley
DOI: 10.1002/ckon.19990060308; 864.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Jensen, Per; Barbe, Alain; Cours, T.
Determination of the Effective Ground State Potential Energy Function of Ozone from High-Resolution Infrared Spectra
Journal of Molecular Spectroscopy, 198 (1) :57-76
1999
DOI: 10.1006/jmsp.1999.7928; 863.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Jensen, Per; Barbe, Alain; Cours, T.
Determination of the Effective Ground State Potential Energy Function of Ozone from High-Resolution Infrared Spectra
Journal of Molecular Spectroscopy, 198 (1) :57-76
1999
DOI: 10.1006/jmsp.1999.7928; 862.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Jensen, Per; Barbe, Alain; Cours, T.
Determination of the Effective Ground State Potential Energy Function of Ozone from High-Resolution Infrared Spectra
Journal of Molecular Spectroscopy, 198 (1) :57-76
1999
DOI: 10.1006/jmsp.1999.7928; 861.
Ehrhardt, Matthias
Discrete transparent boundary conditions for general Schrödinger-type equations
VLSI Design, 9 (4) :325–338
1999
Herausgeber: Hindawi Publishing
DOI: 10.1155/1999/72984; 860.

Discrete transparent boundary conditions for general Schrödinger-type equations
Computer Physics Communications, 121 (4) :598--598
1999
Herausgeber: Hindawi; 859.
[german] Tausch, Michael W.; Grolmuss, A.
Ein low-cost Selbstbau-Spektroskop
Praxis der Naturwissenschaften (Chemie), 48 (7) :36
1999; 858.
Zwart, Hans; Jacob, Birgit
Equivalent conditions for stabilizability of infinite-dimensional systems with admissible control operators
SIAM J. Control Optim., 37 (5) :1419--1455
1999
DOI: 10.1137/S036301299833344X

Index Analysis

Group members working on that field

Cooperations

Publications

882.

881.

880.

879.

878.

877.

876.

875.

874.

873.

872.

871.

870.

869.

868.

867.

866.

865.

864.

863.

862.

861.

860.

859.

858.