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

2001: 982.
Bach, Thorsten; Kirsch, Stefan
Synthesis of 6-Substituted 4-Hydroxy-2-pyrones from Aldehydes by Addition of an Acetoacetate Equivalent, Dess-Martin Oxidation and Subsequent Cyclization
Synlett, 2001 (12) :1974–1976
2001
ISSN: 0936-5214, 1437-2096
DOI: 10.1055/s-2001-18759; 981.
Jacob, Birgit; Partington, Jonathan R.
The Weiss conjecture on admissibility of observation operators for contraction semigroups
Integral Equations Operator Theory, 40 (2) :231--243
2001
DOI: 10.1007/BF01301467; 980.
Bartel, Andreas; Günther, Michael
The developments in multirating for coupled systems
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 81 (S3) :739–742
2001
DOI: 10.1002/zamm.200108115144; 979.
Bartel, A.; G\"unther, Michael
The developments in multirating for coupled systems
Z. f. Angew. Math. u. Mech., 81 (3) :S739--S742
2001; 978.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001
DOI: 10.1006/jmsp.2001.8371; 977.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001
DOI: 10.1006/jmsp.2001.8371; 976.
Yurchenko, Sergey N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Bunker, Philip R.
The near ultraviolet band system of singlet methylene
Journal of Molecular Spectroscopy, 208 (1) :136-143
2001
DOI: 10.1006/jmsp.2001.8371; 975.
Tausch, Michael W.; Wachtendonk, M.
UNTERRICHTSPRAXIS S II, Band 1 ''Protolysegleichgewichte''
Herausgeber: Aulis Verlag Deubner, Köln
2001; 974.
Tausch, Michael W.; Woock, M.; Twellmann, M.
Vom Erdöl zum Kaugummi - ein Kontext und seine Facetten
Praxis der Naturwissenschaften - Chemie in der Schule, 50 (1) :11
2001; 973.
[german] Bohrmann, Claudia; Twellmann, M.; Tausch, Michael W.
Vom galvanischen Element zur Solarzelle
Naturwissenschaften im Unterricht Chemie, 66 (6) :12–16
2001; 972.
Jacob, Birgit
Zeros of Fredholm operator valued H^p-functions
Math. Nachr., 227 :81--97
2001
DOI: 10.1002/1522-2616(200107)227:1<81::AID-MANA81>3.3.CO;2-U
2000: 971.
Günther, Michael
A joint DAE/PDE model for interconnected electrical networks
Mathematical and Computer Modelling of Dynamical Systems, 6 :114–128
2000
Herausgeber: Taylor & Francis
DOI: 10.1076/1387-3954(200006)6:2;1-M;FT114; 970.

A joint DAE/PDE model for interconnected electrical networks
Mathematical and Computer Modelling of Dynamical Systems, 6 (2) :114--128
2000
Herausgeber: Taylor \& Francis; 969.
Garnica, R. M.; Appel, Matthew F.; Eagan, L.; McKeachie, J. Ryan; Benter, Thorsten
A REMPI method for the ultrasensitive detection of NO and NO\(_{2}\) using atmospheric pressure laser ionization mass spectrometry
Analytical Chemistry, 72 (22) :5639-5646
2000
DOI: 10.1021/ac000816i; 968.
Garnica, R. M.; Appel, Matthew F.; Eagan, L.; McKeachie, J. Ryan; Benter, Thorsten
A REMPI method for the ultrasensitive detection of NO and NO\(_{2}\) using atmospheric pressure laser ionization mass spectrometry
Analytical Chemistry, 72 (22) :5639-5646
2000
DOI: 10.1021/ac000816i; 967.
Garnica, R. M.; Appel, Matthew F.; Eagan, L.; McKeachie, J. Ryan; Benter, Thorsten
A REMPI method for the ultrasensitive detection of NO and NO2 using atmospheric pressure laser ionization mass spectrometry
Analytical Chemistry, 72 (22) :5639-5646
2000
DOI: 10.1021/ac000816i; 966.
Gu, Jian-ping; Hirsch, Gerhard; Buenker, Robert J.; Brumm, Martin; Osmann, Gerald; Bunker, Philip R.; Jensen, Per
A theoretical study of the absorption spectrum of singlet CH\(_{2}\)
Journal of Molecular Structure, 517-518 :247-264
2000
DOI: 10.1016/S0022-2860(99)00256-2; 965.
Gu, Jian-ping; Hirsch, Gerhard; Buenker, Robert J.; Brumm, Martin; Osmann, Gerald; Bunker, Philip R.; Jensen, Per
A theoretical study of the absorption spectrum of singlet CH\(_{2}\)
Journal of Molecular Structure, 517-518 :247-264
2000
DOI: 10.1016/S0022-2860(99)00256-2; 964.
Gu, Jian-ping; Hirsch, Gerhard; Buenker, Robert J.; Brumm, Martin; Osmann, Gerald; Bunker, Philip R.; Jensen, Per
A theoretical study of the absorption spectrum of singlet CH2
Journal of Molecular Structure, 517-518 :247-264
2000
DOI: 10.1016/S0022-2860(99)00256-2; 963.
Vander Auwera, J.; Kleffmann, Jörg; Flaud, Jean-Marie; Pawelke, G.; B{ü}rger, H.; Hurtmans, D.; P{é}trisse, R.
Absolute \(\nu\)\(_{2}\) Line Intensities of HOCl by Simultaneous Measurements in the Infrared with a Tunable Diode Laser and Far-Infrared Region Using a Fourier Transform Spectrometer
Journal of Molecular Spectroscopy, 204 (1) :36-47
2000
Herausgeber: Academic Press
DOI: 10.1006/JMSP.2000.8197; 962.
Vander Auwera, J.; Kleffmann, Jörg; Flaud, Jean-Marie; Pawelke, G.; B{ü}rger, H.; Hurtmans, D.; P{é}trisse, R.
Absolute \(\nu\)\(_{2}\) Line Intensities of HOCl by Simultaneous Measurements in the Infrared with a Tunable Diode Laser and Far-Infrared Region Using a Fourier Transform Spectrometer
Journal of Molecular Spectroscopy, 204 (1) :36-47
2000
Herausgeber: Academic Press
DOI: 10.1006/JMSP.2000.8197; 961.
Vander Auwera, J.; Kleffmann, Jörg; Flaud, Jean-Marie; Pawelke, G.; Bürger, H.; Hurtmans, D.; Pétrisse, R.
Absolute ν2 Line Intensities of HOCl by Simultaneous Measurements in the Infrared with a Tunable Diode Laser and Far-Infrared Region Using a Fourier Transform Spectrometer
Journal of Molecular Spectroscopy, 204 (1) :36-47
2000
Herausgeber: Academic Press
DOI: 10.1006/JMSP.2000.8197; 960.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000
DOI: 10.1080/002689700413532; 959.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000
DOI: 10.1080/002689700413532; 958.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000
DOI: 10.1080/002689700413532

Index Analysis

Group members working on that field

Cooperations

Publications

982.

981.

980.

979.

978.

977.

976.

975.

974.

973.

972.

971.

970.

969.

968.

967.

966.

965.

964.

963.

962.

961.

960.

959.

958.