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
- 2000
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
2000963.
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 Press962.
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 Press961.
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 Press960.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000959.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000958.
Jensen, Per
An introduction to the theory of local mode vibrations
Molecular Physics, 98 (17) :1253-1285
2000957.
Günther, Michael; Feldmann, Uwe
CAD based electric circuit modeling in industry. part I: Mathematical structure and index of network equations
2000956.
Becker, Karl Heinz; L{ö}rzer, Jutta C.; Kurtenbach, Ralf; Wiesen, Peter; Jensen, T. E.; Wallington, T. J.
Contribution of vehicle exhaust to the global N\(_{2}\)O budget
Chemosphere - Global Change Science, 2 (3-4) :387-395
2000955.
Becker, Karl Heinz; L{ö}rzer, Jutta C.; Kurtenbach, Ralf; Wiesen, Peter; Jensen, T. E.; Wallington, T. J.
Contribution of vehicle exhaust to the global N\(_{2}\)O budget
Chemosphere - Global Change Science, 2 (3-4) :387-395
2000954.
Becker, Karl Heinz; Lörzer, Jutta C.; Kurtenbach, Ralf; Wiesen, Peter; Jensen, T. E.; Wallington, T. J.
Contribution of vehicle exhaust to the global N2O budget
Chemosphere - Global Change Science, 2 (3-4) :387-395
2000953.
Jacob, Birgit
Corrections to: ``A sufficient condition for exact observability of spectral systems" [Kyungpook Math. J. \bf 35 (1996), no. 3, Special Issue, 427--434; MR1677625 (2000a:93019)] by S. K. Chang and S. M. Hwang
Kyungpook Math. J., 40 (2) :323--325
2000952.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging: The CH\(_{2}\)\(^{+}\), H\(_{2}\)O\(^{+}\) and NH\(_{2}\)\(^{+}\) ions as benchmarks
Chemical Physics Letters, 318 (6) :597-606
2000951.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging: The CH\(_{2}\)\(^{+}\), H\(_{2}\)O\(^{+}\) and NH\(_{2}\)\(^{+}\) ions as benchmarks
Chemical Physics Letters, 318 (6) :597-606
2000950.
Osmann, Gerald; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
Coulomb explosion imaging: The CH2+, H2O+ and NH2+ ions as benchmarks
Chemical Physics Letters, 318 (6) :597-606
2000949.
[german] Tausch, Michael W.; Korn, S.
Der Kohlenstoff-Kreislauf bei der Photosynthese und Atmung als Modellexperiment - Gekoppelte Reaktionszyklen
Praxis der Naturwissenschaften - Chemie in der Schule, 49 (7) :29
2000948.
Tausch, Michael W.
Didaktische Integration - die Versöhnung von Fachsystematik und Alltagsbezug
Chemie in der Schule, 47 (3) :179
2000947.
Günther, M.; Hoschek, M.; Rentrop, P.
Differential-algebraic equations in electric circuit simulation
International Journal of Electronics and Communication (AEÜ), 54 (2) :101–107
2000
Herausgeber: Elsevier946.
Klamroth, Kathrin; Wiecek, Margaret M.
Dynamic programming approaches to the multiple criteria knapsack problem
Naval Research Logistics, 47 :57-76
2000945.
[german] Tausch, Michael W.; Mascia, M.
Ein historisches Experiment 200 Jahre danach: Die Entdeckung der UV-Strahlen durch J. W. Ritter
Naturwissenschaften im Unterricht (Chemie), 57 (17) :117
2000944.
Setzer, Klaus-Dieter; Uibel, C.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and Theoretical Study of the Electronic States and Spectra of BiNa
Journal of Molecular Spectroscopy, 204 (2) :163-175
2000
Herausgeber: Academic Press943.
Setzer, Klaus-Dieter; Uibel, C.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and Theoretical Study of the Electronic States and Spectra of BiNa
Journal of Molecular Spectroscopy, 204 (2) :163-175
2000
Herausgeber: Academic Press942.
Setzer, Klaus-Dieter; Uibel, C.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and Theoretical Study of the Electronic States and Spectra of BiNa
Journal of Molecular Spectroscopy, 204 (2) :163-175
2000
Herausgeber: Academic Press941.
Bartel, A.
Generalised Multirate — Two {ROW}-type Versions for Circuit simulation
Unclas- sified NatLab Report No. 2000/804
Herausgeber: Philips Electronics
2000940.
Bartel, A
Generalised multirate: Two {ROW}-type versions for circuit simulation
Unclassified NatLab Report, Eindhoven, 804 :2000
2000
