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

1990

304.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH\(_{2}\)
Molecular Physics, 70 (3) :443-454
1990

DOI: 10.1080/00268979000101111

303.

Jensen, Per; Buenker, Robert J.; Hirsch, Gerhard; Rai, Sachchida N.
An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2
Molecular Physics, 70 (3) :443-454
1990

DOI: 10.1080/00268979000101111

302.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

301.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

300.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Kofranek, Manfred; Lischka, Hans
An ab initio calculation of the stretching energies for the HF dimer
The Journal of Chemical Physics, 92 (12) :7432-7440
1990

DOI: 10.1063/1.458229

299.

Heilmann, Margareta; Müller, Manfred
Direct and converse results on simultaneous approximation by the method of Bernstein-Durrmeyer operators
Algorithms for approximation II, Proc. 2nd Int. Conf., Shrivenham/UK 1988, Seite 107-116
1990

DOI: 10.1007/978-1-4899-3442-0_11

298.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

297.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a\(^{1}\)\(\Delta\)\(_{g}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\), b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) and X\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\) systems of O\(_{2}\), SO, S\(_{2}\) and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

296.

Fink, Ewald H.; Kruse, H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High resolution Fourier-transform spectra of the a1Δg → X3Σg-, b1Σg+ → X3Σg- and X1Σg+ → a1Δg systems of O2, SO, S2 and isoe
Acta Physica Hungarica, 67 (1-2) :67-72
1990

DOI: 10.1007/BF03054252

295.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

294.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0\(^{+}\) emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

293.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Brown, John M.
High-resolution study of the A 1-X 0+ emission system of bismuth hydride
Journal of Molecular Spectroscopy, 142 (1) :108-116
1990

DOI: 10.1016/0022-2852(90)90294-Z

292.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse)
Herausgeber: C. C. Buchner, Bamberg
1990

291.

Tausch, Michael W.; Deissenberger, H.; Fischer, W.; Hoffmann, W.; Jakob, O.; Riedl, A.; Schallies, M.; Wachtendonk, M.
STOFF UND FORMEL II, Lehrbuch für die S II (Grundkurse), 325 Seiten
Herausgeber: C. C. Buchner, Bamberg
1990

290.


Technische Universität Berlin Wintersemester 06/07 Fakultät II--Institut für Mathematik
SIAM J. Appl. Math, 50 :1442--1456
1990
1989

289.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

288.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

287.

Bunker, Philip R.; Jensen, Per; Karpfen, Alfred; Lischka, Hans
A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH
Journal of Molecular Spectroscopy, 135 (1) :89-104
1989

DOI: 10.1016/0022-2852(89)90357-3

286.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

285.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

284.

Comeau, Donald C.; Shavitt, Isaiah; Jensen, Per; Bunker, Philip R.
An ab initio determination of the potential-energy surfaces and rotation-vibration energy levels of methylene in the lowest triplet and singlet states and the singlet-triplet splitting
The Journal of Chemical Physics, 90 (11) :6491-6500
1989

DOI: 10.1063/1.456315

283.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH\(^{+}\)
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

282.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH\(^{+}\)
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

281.

Civis, S.; Blom, C. E.; Jensen, Per
Diode laser infrared spectra and potential energy curve for SH+
Journal of Molecular Spectroscopy, 138 (1) :69-78
1989

DOI: 10.1016/0022-2852(89)90099-4

280.

Heilmann, Margareta
Direct and converse results for operators of Baskakov-Durrmeyer type
Approximation Theory Appl., 5 (1) :105-127
1989

DOI: 10.1007/BF02836120