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
- 1987
202.
Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987201.
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
1987200.
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
1987199.
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
1987198.
[german] Tausch, Michael W.
Photochemische cis-trans Isomerisierungen
Der mathematische und naturwissenschaftliche Unterricht (MNU), 40 :92
1987197.
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
1987196.
Tausch, Michael W.; Fischer, W.; Glöckner, W.; Köhler-Degner, M.; Nöding, S.; Wolf, H.
STOFF UND FORMEL - Chemiebuch für Gymnasien; Ausgabe NRW, S I, 291 Seiten
Herausgeber: C. C. Buchner, Bamberg
1987195.
Tausch, Michael W.; Fischer, W.; Glöckner, W.; Köhler-Degner, M.; Nöding, S.; Wolf, H.
STOFF UND FORMEL - Lehrerbände mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL - Chemiebuch für Gymnasien und Ausgabe NRW
Herausgeber: C. C. Buchner, Bamberg
1987194.
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
1987193.
Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC+
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987192.
Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987191.
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
1987190.
Heilmann, Margareta
Approximation auf [0, ∞) durch das Verfahren der Operatoren vom Baskakov-Durrmeyer Typ
Universität Dortmund
1987189.
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
1987188.
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
1987187.
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
1987186.
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
1987185.
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
1987184.
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
1987183.
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
1987182.
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
1987181.
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- 1986
180.
Fink, Ewald H.; Kruse, H.; Ramsay, D. A.
The high-resolution emission spectrum of S\(_{2}\) in the near infrared: The b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) - X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) system
Journal of Molecular Spectroscopy, 119 (2) :377-387
1986179.
Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H2O and C3 calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986178.
Jensen, Per; Johns, John W. C.
The infrared spectrum of carbon suboxide in the ν6 fundamental region: Experimental observation and semirigid bender analysis
Journal of Molecular Spectroscopy, 118 (1) :248-266
1986
