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
- 1995
561.
Denk, Ceorg; Günther, Michael; Kahlert, Martin; Paffrath, Meinhard; Rentrop, Peter; Wever, Utz; Zheng, Q
Recent advances in electronic industry by numerical simulation
Preprint (1784)
1995
Herausgeber: Technische Hochschule Darmstadt560.
Heilmann, Margareta
Saturation of linear combinations of Baskakov-Durrmeyer-type operators
Applicable Analysis, 59 (1-4) :93-107
1995559.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Temperature and pressure dependence of the NCO + C\(_{2}\)H\(_{2}\) reaction
Chemical Physics Letters, 235 (3-4) :230-234
1995558.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Temperature and pressure dependence of the NCO + C\(_{2}\)H\(_{2}\) reaction
Chemical Physics Letters, 235 (3-4) :230-234
1995557.
Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Temperature and pressure dependence of the NCO + C2H2 reaction
Chemical Physics Letters, 235 (3-4) :230-234
1995556.
G\"unther, Michael; Feldmann, U.
The {DAE}-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 :573--582
1995555.
Günther, Michael; Feldmann, Uwe
The DAE-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 (5) :573–582
1995
Herausgeber: Elsevier554.
Günther, Michael; Feldmann, Uwe
The DAE-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 (5-6) :573--582
1995
Herausgeber: North-Holland553.
Shestakov, Oleg; Fink, Ewald H.
The Lowest Quartet States, a\(^{4}\)\(\Pi\) and b\(^{4}\)\(\Sigma\)\(^{-}\), of SbO
Journal of Molecular Spectroscopy, 172 (1) :215-224
1995
Herausgeber: Academic Press552.
Shestakov, Oleg; Fink, Ewald H.
The Lowest Quartet States, a\(^{4}\)\(\Pi\) and b\(^{4}\)\(\Sigma\)\(^{-}\), of SbO
Journal of Molecular Spectroscopy, 172 (1) :215-224
1995
Herausgeber: Academic Press551.
Shestakov, Oleg; Fink, Ewald H.
The Lowest Quartet States, a4Π and b4Σ-, of SbO
Journal of Molecular Spectroscopy, 172 (1) :215-224
1995
Herausgeber: Academic Press550.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS\(_{2}\) Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press549.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS\(_{2}\) Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press548.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS2 Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press547.
Denk, Georg; Feldmann, Uwe; Günther, Michael; Rentrop, Peter
Topics in electric circuit simulation
Preprint (1740)
1995
Herausgeber: Technische Hochschule Darmstadt546.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH\(_{3}\)OBr; Br(\(^{2}\)P\(_{3/2}\)) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995545.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH\(_{3}\)OBr; Br(\(^{2}\)P\(_{3/2}\)) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995544.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH3OBr; Br(2P3/2) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995543.
Günther, M.; Lehn, J.; Rentrop, P.; Rettig, S.; Simeon, B.
Wissenschaftliches Rechnen aus der Sicht der Mathematik
Thema Forschung 2/95, 2 :26–35
1995
Herausgeber: Technische Hochschule Darmstadt542.
G\"unther, Michael; Lehn, J.; Rentrop, P.; Rettig, S.; Simeon, B.
Wissenschaftliches Rechnen aus der Sicht der Mathematik
Thema Forschung 2/95, TH Darmstadt, 2 :26--35
1995- 1994
541.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press540.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press539.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press538.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
A spectroscopically determined potential energy surface for the ground state of H\(_{2}\)\(^{16}\)O: A new level of accuracy
The Journal of Chemical Physics, 101 (9) :7651-7657
1994537.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
A spectroscopically determined potential energy surface for the ground state of H\(_{2}\)\(^{16}\)O: A new level of accuracy
The Journal of Chemical Physics, 101 (9) :7651-7657
1994
