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

1988

207.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

206.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

205.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X~3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

1987

204.

Spirko, Vladim{í}r; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

203.

Spirko, Vladim{í}r; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

202.

Spirko, Vladimír; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H3+: Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

201.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of \(\nu\)\(_{1}\) and \(\nu\)\(_{3}\) for triplet methylene (X\verb=~=\(^{3}\)B\(_{1}\) CH\(_{2}\)) and the determination of the vibrationless singlet-triplet splitting Te (a\verb=~=\(^{1}\)A\(_{1}\))
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

200.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of \(\nu\)\(_{1}\) and \(\nu\)\(_{3}\) for triplet methylene (X\verb=~=\(^{3}\)B\(_{1}\) CH\(_{2}\)) and the determination of the vibrationless singlet-triplet splitting Te (a\verb=~=\(^{1}\)A\(_{1}\))
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

199.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH\(_{2}\)\(^{+}\) using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

198.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH\(_{2}\)\(^{+}\) using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

197.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH2+ using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

196.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of ν1 and ν3 for triplet methylene (X~3B1 CH2) and the determination of the vibrationless singlet-triplet splitting Te (a~1A1)
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

195.

Heilmann, Margareta
Approximation auf [0, ∞) durch das Verfahren der Operatoren vom Baskakov-Durrmeyer Typ
Universität Dortmund
1987

194.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987

DOI: 10.1016/0022-2852(87)90061-0

193.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987

DOI: 10.1016/0022-2852(87)90061-0

192.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC+
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987

DOI: 10.1016/0022-2852(87)90061-0

191.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Wang, Ding Chang
High resolution studies of the b\(^{1}\)\(\Sigma\)\(^{+}\) - X\(^{3}\)\(\Sigma\) emission system of SeS
Molecular Physics, 60 (2) :277-290
1987

DOI: 10.1080/00268978700100221

190.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Wang, Ding Chang
High resolution studies of the b\(^{1}\)\(\Sigma\)\(^{+}\) - X\(^{3}\)\(\Sigma\) emission system of SeS
Molecular Physics, 60 (2) :277-290
1987

DOI: 10.1080/00268978700100221

189.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Wang, Ding Chang
High resolution studies of the b1Σ+ - X3Σ emission system of SeS
Molecular Physics, 60 (2) :277-290
1987

DOI: 10.1080/00268978700100221

188.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High-resolution study of the emission system of \(^{80}\)SeO
Journal of Molecular Spectroscopy, 125 (1) :66-75
1987

DOI: 10.1016/0022-2852(87)90193-7

187.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High-resolution study of the emission system of \(^{80}\)SeO
Journal of Molecular Spectroscopy, 125 (1) :66-75
1987

DOI: 10.1016/0022-2852(87)90193-7

186.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
High-resolution study of the emission system of 80SeO
Journal of Molecular Spectroscopy, 125 (1) :66-75
1987

DOI: 10.1016/0022-2852(87)90193-7

185.

Franik, R.; Tausch, Michael W.; Autorenteam
KLAUSUR- UND ABITURTRAINING CHEMIE, Aufgabensammlung mit Lösungen und weiterführenden Informationen für die S II, 7 Bände
Herausgeber: Aulis Deubner\&Co KG, Köln
1987

184.

[german] Tausch, Michael W.
Photochemische cis-trans Isomerisierungen
Der mathematische und naturwissenschaftliche Unterricht (MNU), 40 :92
1987

183.

Tausch, Michael W.; Fischer, W.; Glöckner, W.; Köhler-Degner, M.; Nöding, S.; Wolf, H.
STOFF UND FORMEL - Chemiebuch für Gymnasien, S I, 291 Seiten
Herausgeber: C. C. Buchner, Bamberg
1987