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
- 1997
702.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press701.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab Initio Study of the NH\(_{2}\)\(^{+}\) Absorption Spectrum
Journal of Molecular Spectroscopy, 186 (2) :319-334
1997700.
Kozin, Igor N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Hirsch, Gerhard; Klee, Stefan
An ab initio calculation of the dipole moment surfaces and the vibrational transition moments of the H2Te molecule
Journal of Molecular Spectroscopy, 181 (1) :108-118
1997
Herausgeber: Academic Press699.
Kozin, Igor N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Hirsch, Gerhard; Klee, Stefan
An ab initio calculation of the dipole moment surfaces and the vibrational transition moments of the H\(_{2}\)Te molecule
Journal of Molecular Spectroscopy, 181 (1) :108-118
1997
Herausgeber: Academic Press698.
Kozin, Igor N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Hirsch, Gerhard; Klee, Stefan
An ab initio calculation of the dipole moment surfaces and the vibrational transition moments of the H\(_{2}\)Te molecule
Journal of Molecular Spectroscopy, 181 (1) :108-118
1997
Herausgeber: Academic Press697.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH2+
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland696.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH\(_{2}\)\(^{+}\)
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland695.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH\(_{2}\)\(^{+}\)
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland694.
Gómez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H2Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press693.
G{{\'o}}mez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H\(_{2}\)Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press692.
G{{\'o}}mez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H\(_{2}\)Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press691.
Ehrgott, Matthias; Hamacher, Horst W.; Klamroth, Kathrin; Nickel, Stefan; Schöbel, Anita; Wiecek, Margaret M.
A note on the equivalence of balance points and Pareto solutions in multiple objective programming
Journal of Optimization Theory and Applications, 92 :209-212
1997690.
Arnold, A.; Ehrhardt, M.
A New Discrete Transparent Boundary Condition for Standard and Wide Angle 'Parabolic' Equations in Underwater Acoustics
Proceedings of the Third International Conference on Theoretical and Computational Acoustics, July 14-18, 1997, Newark, New Jersey, USA, Seite 623-635
1997689.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press688.
Gómez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H2Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press687.
Jensen, Per; Sauer, Stephan P. A.
Theoretical calculations of the hyperfine structure in the spectra of H\(_{3}\)\(^{+}\) and its deuterated isotopomers
Molecular Physics, 91 (2) :319-332
1997686.
Schindler, J. G.; Schindler, M. M.; Herna, K.; Kling, H.-W.
Glutardialdehyde and formaldehyde biosensors
Biomed. Tech. (Berl), 42 (9) :264
1997685.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press684.
Kozin, Igor N.; Jensen, Per
The Effects of Nonzero Total Electron Spin in the X\verb=~= \(^{3}\)B\(_{1}\) State of Methylene CH\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :398-406
1997
Herausgeber: Academic Press683.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its 1B2 electronic state
Molecular Physics, 91 (4) :653-662
1997682.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997681.
Bludsky, Ota; Jensen, Per
The calculation of the bound and quasibound vibrational states for ozone in its \(^{1}\)B\(_{2}\) electronic state
Molecular Physics, 91 (4) :653-662
1997680.
Tausch, Michael W.
Simulation von chemischen Gleichgewichten
Computer + Unterricht, 26 :35
1997679.
Günther, Michael; Hoschek, Markus
ROW methods adapted to electric circuit simulation packages
Journal of computational and applied mathematics, 82 (1-2) :159--170
1997
Herausgeber: North-Holland678.
Schryber, Jeremy H.; Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
On the spectroscopically determined potential energy surfaces for the electronic ground states of NO2 and H2O
Journal of Molecular Spectroscopy, 185 (2) :234-243
1997
Herausgeber: Academic Press
