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

1987

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

182.

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
1987

181.

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
1987
1986

180.

Maten, E. Jan W.; Sleijpen, Gerard L. G.
A convergence analysis of Hopscotch methods for fourth order parabolic equations
Numerische Mathematik, 49 (2-3) :275--290
März 1986
Herausgeber: Springer Science and Business Media {LLC}

DOI: 10.1007/bf01389630

179.

Jensen, Per; Spirko, Vladim{í}r
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

178.

Jensen, Per; Spirko, Vladim{í}r
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

177.

Jensen, Per; Spirko, Vladim{í}r; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Extension to H\(_{2}\)D\(^{+}\) and D\(_{2}\)H\(^{+}\)
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

176.

Jensen, Per; Spirko, Vladim{í}r; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Extension to H\(_{2}\)D\(^{+}\) and D\(_{2}\)H\(^{+}\)
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

175.

Jensen, Per; Spirko, Vladimír
A new Morse-oscillator based Hamiltonian for H3+: Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

174.

Jensen, Per; Spirko, Vladimír; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H3+: Extension to H2D+ and D2H+
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

173.

Adams, Warren P; Sherali, Hanif D
A tight linearization and an algorithm for zero-one quadratic programming problems
Management Science, 32 (10) :1274--1290
1986
Herausgeber: INFORMS

172.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

171.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

170.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC+ calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

169.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8

168.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8