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

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

279.

Heilmann, Margareta; Müller, Manfred
Direct and converse results on weighted simultaneous approximation by the method of operators of Baskakov-Durrmeyer type
Results in Mathematics, 16 (3-4) :228-242
1989

DOI: 10.1007/BF03322474

278.

Tausch, Michael W.; Wöhrle, D.
Katalytische Wasserphotolyse
Praxis der Naturwissenschaften (Chemie), 38 :46
1989

277.

Tausch, Michael W.
Kritische Überlegungen zur Teilchenzahl als eigenständige Größe im Größenkalkül
Der mathematische und naturwissenschaftliche Unterricht (MNU), 42 :438
1989

276.

Tausch, Michael W.; Wachtendonk, M.
Lehrerband mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF-FORMEL-UMWELT, BAND 1: CHEMISCHE GLEICHGEWICHTE - ELEKTROCHEMIE, Lehrbuch für die S II (Grund- und Leistungskurse), 172 Seiten
Herausgeber: C. C. Buchner, Bamberg
1989

275.

Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A\(^{2}\)\(\Delta\), v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989

DOI: 10.1016/0009-2614(89)87344-0

274.

Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A\(^{2}\)\(\Delta\), v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989

DOI: 10.1016/0009-2614(89)87344-0

273.

Bauer, W.; Engelhardt, B.; Wiesen, Peter; Becker, Karl Heinz
Lifetime measurements of GeH and CH in the A2Δ, v'=0 state by laser-induced fluorescence
Chemical Physics Letters, 158 (3-4) :321-324
1989

DOI: 10.1016/0009-2614(89)87344-0

272.

Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A\(^{2}\)\(\Delta\) → X\(^{2}\)\(\Pi\)) Chemiluminescence in the C\(_{2}\)H\(_{2}\) + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989

DOI: 10.1524/zpch.1989.161.Part_1_2.131

271.

Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A\(^{2}\)\(\Delta\) → X\(^{2}\)\(\Pi\)) Chemiluminescence in the C\(_{2}\)H\(_{2}\) + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989

DOI: 10.1524/zpch.1989.161.Part_1_2.131

270.

Becker, Karl Heinz; Wiesen, Peter
Measurements on the CH*(A2Δ → X2Π) Chemiluminescence in the C2H2 + O Flame and Quenching Rate Constants for Different Reactants at 297 K
Zeitschrift für Physikalische Chemie, 161 (Part_1_2) :131-144
1989

DOI: 10.1524/zpch.1989.161.Part_1_2.131

269.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

268.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

267.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

266.

Heilmann, Margareta
On simultaneous approximation by optimal algebraic polynomials
Results in Mathematics, 16 (1-2) :77-81
1989

DOI: 10.1007/BF03322645

265.

Heilmann, Margareta; Müller, Manfred
On simultaneous approximation by the method of Baskakov-Durrmeyer operators
Numerical Functional Analysis and Optimization, 10 (1-2) :127-138
1989

DOI: 10.1080/01630568908816295