Applied and Computational Mathematics (ACM)

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

575.

Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter; Febo, Antonio; Gherardi, M.; Sparapani, R.
Line strength measurements of trans-HONO near 1255 cm\(^{-1}\) by tunable diode laser spectrometry
Geophysical Research Letters, 22 (18) :2485-2488
1995
Herausgeber: John Wiley \& Sons, Ltd

574.

Becker, Karl Heinz; Kleffmann, Jörg; Kurtenbach, Ralf; Wiesen, Peter; Febo, Antonio; Gherardi, M.; Sparapani, R.
Line strength measurements of trans-HONO near 1255 cm-1 by tunable diode laser spectrometry
Geophysical Research Letters, 22 (18) :2485-2488
1995
Herausgeber: John Wiley & Sons, Ltd

573.

Jacob, Birgit
Linear quadratic optimal control of time-varying systems with indefinite costs on Hilbert spaces: the finite horizon problem
J. Math. Systems Estim. Control, 5 (1) :28
1995

572.

Benter, Thorsten; Liesner, M.; Sauerland, V.; Schindler, Ralph N.
Mass spectrometric in-situ determination of NO\(_{2}\) in gas mixtures by resonance enhanced multiphoton ionisation
Fresenius' Journal of Analytical Chemistry, 351 (6) :489-492
1995

571.

Benter, Thorsten; Liesner, M.; Sauerland, V.; Schindler, Ralph N.
Mass spectrometric in-situ determination of NO\(_{2}\) in gas mixtures by resonance enhanced multiphoton ionisation
Fresenius' Journal of Analytical Chemistry, 351 (6) :489-492
1995

570.

Benter, Thorsten; Liesner, M.; Sauerland, V.; Schindler, Ralph N.
Mass spectrometric in-situ determination of NO2 in gas mixtures by resonance enhanced multiphoton ionisation
Fresenius' Journal of Analytical Chemistry, 351 (6) :489-492
1995

569.

Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Mechanistic study of the heterogeneous conversion of NO\(_{2}\) into HONO and N\(_{2}\)O on acid surfaces
Faraday Discussions, 100 (2) :121-127
1995

568.

Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Mechanistic study of the heterogeneous conversion of NO\(_{2}\) into HONO and N\(_{2}\)O on acid surfaces
Faraday Discussions, 100 (2) :121-127
1995

567.

Wiesen, Peter; Kleffmann, Jörg; Kurtenbach, Ralf; Becker, Karl Heinz
Mechanistic study of the heterogeneous conversion of NO2 into HONO and N2O on acid surfaces
Faraday Discussions, 100 (2) :121-127
1995

566.

Denk, Georg; Feldmann, Uwe; Günther, Michael
Modeling and simulating charge sensitive MOS circuits
1995

565.

Bunker, Philip R.; Kolbuszewski, M.; Jensen, Per; Brumm, Martin; Anderson, M. A.; Barclay, W. L.; Ziurys, L. M.; Ni, Y.; Harris, David O.
New rovibrational data for MgOH and MgOD and the internuclear potential function of the ground electronic state
Chemical Physics Letters, 239 (4-6) :217-222
1995

564.

Bunker, Philip R.; Kolbuszewski, M.; Jensen, Per; Brumm, Martin; Anderson, M. A.; Barclay, W. L.; Ziurys, L. M.; Ni, Y.; Harris, David O.
New rovibrational data for MgOH and MgOD and the internuclear potential function of the ground electronic state
Chemical Physics Letters, 239 (4-6) :217-222
1995

563.

Bunker, Philip R.; Kolbuszewski, M.; Jensen, Per; Brumm, Martin; Anderson, M. A.; Barclay, W. L.; Ziurys, L. M.; Ni, Y.; Harris, David O.
New rovibrational data for MgOH and MgOD and the internuclear potential function of the ground electronic state
Chemical Physics Letters, 239 (4-6) :217-222
1995

562.

Günther, Michael; Simeon, Bernd
Praktikum Wissenschaftliches Rechnen auf dem HRZ-Vektorparallelrechner VPP
Preprint (1785)
1995
Herausgeber: Technische Hochschule Darmstadt

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 Darmstadt

560.

Heilmann, Margareta
Saturation of linear combinations of Baskakov-Durrmeyer-type operators
Applicable Analysis, 59 (1-4) :93-107
1995

559.

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
1995

558.

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
1995

557.

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
1995

556.

G\"unther, Michael; Feldmann, U.
The {DAE}-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 :573--582
1995

555.

Günther, Michael; Feldmann, Uwe
The DAE-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 (5) :573–582
1995
Herausgeber: Elsevier

554.

Günther, Michael; Feldmann, Uwe
The DAE-index in electric circuit simulation
Mathematics and Computers in Simulation, 39 (5-6) :573--582
1995
Herausgeber: North-Holland

553.

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 Press

552.

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 Press

551.

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 Press