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
- 1991
362.
Jensen, Per; Bunker, Philip R.; Karpfen, Alfred
An ab initio calculation of the nonadiabatic effect on the tunneling splitting in vibrationally excited (HF)2
Journal of Molecular Spectroscopy, 148 (2) :385-390
1991361.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991360.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991359.
Jensen, Per; Marshall, Mark D.; Bunker, Philip R.; Karpfen, Alfred
An ab initio close-coupling calculation of the lower vibrational energies of the HCl dimer
Chemical Physics Letters, 180 (6) :594-600
1991358.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991357.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991356.
Marshall, Mark D.; Jensen, Per; Bunker, Philip R.
An ab initio close-coupling calculation of the lower vibrational energies of the HF dimer
Chemical Physics Letters, 176 (3-4) :255-260
1991355.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991354.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991353.
Karpfen, Alfred; Bunker, Philip R.; Jensen, Per
An ab initio study of the hydrogen chloride dimer: the potential energy surface and the characterization of the stationary points
Chemical Physics, 149 (3) :299-309
1991352.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991351.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991350.
Bunker, Philip R.; Epa, V. C.; Jensen, Per; Karpfen, Alfred
An analytical ab initio potential surface and the calculated tunneling energies for the HCl dimer
Journal of Molecular Spectroscopy, 146 (1) :200-219
1991349.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991348.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, J{ü}rgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) → a\(^{1}\)\(\Delta\)\(_{g}\)) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991347.
Fink, Ewald H.; Setzer, Klaus-Dieter; Wildt, Jürgen; Ramsay, D. A.; Vervloet, M.
Collision-induced emission of O2(b1Σg+ → a1Δg) in the gas phase
International Journal of Quantum Chemistry, 39 (3) :287-298
1991346.
Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991345.
Vilesov, A. F.; Wildt, J{ü}rgen; Fink, Ewald H.
Emission of Xe: N(\(^{2}\)P) collision complexes near the N(\(^{2}\)P→\(^{2}\)D) lines
Chemical Physics, 153 (3) :531-537
1991344.
Vilesov, A. F.; Wildt, Jürgen; Fink, Ewald H.
Emission of Xe: N(2P) collision complexes near the N(2P→2D) lines
Chemical Physics, 153 (3) :531-537
1991343.
Heilmann, Margareta; Müller, Manfred
Equivalence of a weighted modulus of smoothness and a modified weighted K-functional
In Nevai, P. and Pinkus, A., Editor
Herausgeber: Academic Press
1991342.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991341.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991340.
Jensen, Per; Oddershede, Jens; Sabin, John R.
Geometric dependence of the mean excitation energy and spectral moments of water
Physical Review A, 43 (7) :4040-4043
1991339.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991338.
Becker, Karl Heinz; Geiger, Harald; Wiesen, Peter
Kinetic study of the OH radical chain in the reaction system OH + C\(_{2}\)H\(_{4}\) + NO + air
Chemical Physics Letters, 184 (4) :256-261
1991
