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
- 1996
675.
Gu, Jian-ping; Buenker, Robert J.; Hirsch, Gerhard; Jensen, Per; Bunker, Philip R.
An ab Initio Calculation of BH\(_{2}\)\(^{-}\) Rovibronic Energies: A Very Small Singlet-Triplet Splitting
Journal of Molecular Spectroscopy, 178 (2) :172-183
1996
Herausgeber: Academic Press674.
Gu, Jian-ping; Buenker, Robert J.; Hirsch, Gerhard; Jensen, Per; Bunker, Philip R.
An ab Initio Calculation of BH2- Rovibronic Energies: A Very Small Singlet-Triplet Splitting
Journal of Molecular Spectroscopy, 178 (2) :172-183
1996
Herausgeber: Academic Press673.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH\(_{2}\) molecule
Molecular Physics, 88 (1) :105-124
1996672.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH\(_{2}\) molecule
Molecular Physics, 88 (1) :105-124
1996671.
Kolbuszewski, M.; Bunker, Philip R.; Kraemer, Wolfgang P.; Osmann, Gerald; Jensen, Per
An ab initio calculation of the rovibronic energies of the BH2 molecule
Molecular Physics, 88 (1) :105-124
1996670.
Jacob, Birgit
Destabilization of infinite-dimensional time-varying systems via dynamical output feedback
, Recent developments in operator theory and its applications (<prt>W</prt>innipeg, <prt>MB</prt>, 1994) Band 87 aus Oper. Theory Adv. Appl.
Seite 193--206
Herausgeber: Birkhäuser, Basel
1996
193--206669.
Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Emission of nitrous oxide and methane from aero engines: Monitoring by tunable diode laser spectroscopy
Infrared Physics and Technology, 37 (1) :75-81
1996
Herausgeber: Pergamon668.
Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Emission of nitrous oxide and methane from aero engines: Monitoring by tunable diode laser spectroscopy
Infrared Physics and Technology, 37 (1) :75-81
1996
Herausgeber: Pergamon667.
Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Emission of nitrous oxide and methane from aero engines: Monitoring by tunable diode laser spectroscopy
Infrared Physics and Technology, 37 (1) :75-81
1996
Herausgeber: Pergamon666.
Hamacher, Horst W.; Klamroth, Kathrin; Nickel, Stefan
EWGLA 8 Proceedings
Band 10 aus Special Issue of Studies in Locational Analysis
1996665.
Bunker, Philip R.; Jensen, Per; Yamaguchi, Yukio; Schaefer, Henry F.
High-level ab initio calculation of the rotation-vibration energies in the c\verb=~= \(^{1}\)A\(_{1}\) state of methylene, CH\(_{2}\)
Journal of Physical Chemistry, 100 (46) :18088-18092
1996664.
Bunker, Philip R.; Jensen, Per; Yamaguchi, Yukio; Schaefer, Henry F.
High-level ab initio calculation of the rotation-vibration energies in the c\verb=~= \(^{1}\)A\(_{1}\) state of methylene, CH\(_{2}\)
Journal of Physical Chemistry, 100 (46) :18088-18092
1996663.
Bunker, Philip R.; Jensen, Per; Yamaguchi, Yukio; Schaefer, Henry F.
High-level ab initio calculation of the rotation-vibration energies in the c~ 1A1 state of methylene, CH2
Journal of Physical Chemistry, 100 (46) :18088-18092
1996662.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press661.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X\(_{2}\)1 → X\(_{1}\)0\(^{+}\) Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press660.
Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Towle, J. P.; Brown, John M.
High-Resolution Study of the X21 → X10+ Fine-Structure Transition of BiF
Journal of Molecular Spectroscopy, 178 (2) :143-156
1996
Herausgeber: Academic Press659.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N\(_{2}\) [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996658.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N\(_{2}\) [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996657.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetics of the reaction CH + N2 [M]→ Products in the range 10-620 torr and 298-1059 K
International Journal of Chemical Kinetics, 28 (2) :115-123
1996656.
G\"unther, Michael; Denk, G.; Feldmann, U.
Modeling and simulating charge sensitive {MOS} circuits
Math. Modelling of Systems, 2 :69--81
1996655.
Günther, Michael; Denk, Georg; Feldmann, Uwe
Modeling and simulating charge sensitive MOS circuits
Mathematical Modelling of Systems, 2 (1) :69–81
1996
Herausgeber: Taylor & Francis654.
Denk, G; Feldmann, U
Modelling and simulating charge sensitive MOS circuits
Mathematical Modelling of Systems, 2 (1) :69--81
1996
Herausgeber: Taylor \& Francis653.
Günther, Michael; Hoschek, Markus
Modified ROW methods for electric circuit simulation packages
Preprint (1864)
1996
Herausgeber: Technische Hochschule Darmstadt652.
Günther, Michael
Numerical solution of differential-algebraic equations in electric circuit simulation
In Neunzert, Helmut, Editor
Seite 285–294
Herausgeber: Vieweg+ Teubner
1996
285–294651.
Günther, Michael
Numerical solution of differential-algebraic equations in electric circuit simulation
Progress in Industrial Mathematics at ECMI 94 :285--294
1996
Herausgeber: Vieweg+ Teubner Verlag
