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
- 2002
1143.
Mannschreck, K.; B{ä}chmann, K.; Becker, Karl Heinz; Heil, Th.; Kurtenbach, Ralf; Memmesheimer, M.; Mohnen, V.; Obermeier, A.; Poppe, Dirk; Steinbrecher, R.; Schmitz, Th.; Volz-Thomas, A.; Zabel, Friedhelm
A database for volatile organic compounds
Journal of Atmospheric Chemistry, 42 (1-3) :281-286
20021142.
Mannschreck, K.; Bächmann, K.; Becker, Karl Heinz; Heil, Th.; Kurtenbach, Ralf; Memmesheimer, M.; Mohnen, V.; Obermeier, A.; Poppe, Dirk; Steinbrecher, R.; Schmitz, Th.; Volz-Thomas, A.; Zabel, Friedhelm
A database for volatile organic compounds
Journal of Atmospheric Chemistry, 42 (1-3) :281-286
20021141.
Pulch, R.; Günther, M.
A method of characteristics for solving multirate partial differential equations in radio frequency application
Applied Numerical Mathematics, 42 (1) :397–409
2002
Herausgeber: Elsevier1140.
Pulch, Roland; Günther, Michael
A method of characteristics for solving multirate partial differential equations in radio frequency application
Applied numerical mathematics, 42 (1-3) :397--409
2002
Herausgeber: North-Holland1139.
Bartel, Andreas; Günther, Michael
A multirate W-method for electrical networks in state-space formulation
Journal of Computational and Applied Mathematics, 147 (2) :411–425
2002
Herausgeber: Elsevier1138.
Bartel, A.; G\"unther, Michael
A multirate W-method for electrical networks in state-space formulation
Comp.~Appl.~Math., 147 (2) :411--425
20021137.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
A theoretical study of A\verb=~=\(^{2}\)\(\Pi\) MgCN
Journal of Molecular Spectroscopy, 216 (2) :379-396
20021136.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
A theoretical study of A\verb=~=\(^{2}\)\(\Pi\) MgCN
Journal of Molecular Spectroscopy, 216 (2) :379-396
20021135.
Jensen, Per; Wesolowski, Steven S.; Brinkmann, Nicole R.; Richardson, Nancy A.; Yamaguchi, Yukio; Schaefer, Henry F.; Bunker, Philip R.
A Theoretical Study of a\verb=~=\(^{4}\)A\(_{2}\) CH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 211 (2) :254-261
20021134.
Jensen, Per; Wesolowski, Steven S.; Brinkmann, Nicole R.; Richardson, Nancy A.; Yamaguchi, Yukio; Schaefer, Henry F.; Bunker, Philip R.
A Theoretical Study of a\verb=~=\(^{4}\)A\(_{2}\) CH\(_{2}\)\(^{+}\)
Journal of Molecular Spectroscopy, 211 (2) :254-261
20021133.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
A theoretical study of A~2Π MgCN
Journal of Molecular Spectroscopy, 216 (2) :379-396
20021132.
Jensen, Per; Wesolowski, Steven S.; Brinkmann, Nicole R.; Richardson, Nancy A.; Yamaguchi, Yukio; Schaefer, Henry F.; Bunker, Philip R.
A Theoretical Study of a~4A2 CH2+
Journal of Molecular Spectroscopy, 211 (2) :254-261
20021131.
Hirano, Tsuneo; Ishii, Keisaku; Odaka, Tina Erica; Jensen, Per
A Theoretical Study of MgNC and MgCN in the X\verb=~=\(^{2}\)\(\Sigma\)\(^{+}\) Electronic State
Journal of Molecular Spectroscopy, 215 (1) :42-57
20021130.
Hirano, Tsuneo; Ishii, Keisaku; Odaka, Tina Erica; Jensen, Per
A Theoretical Study of MgNC and MgCN in the X\verb=~=\(^{2}\)\(\Sigma\)\(^{+}\) Electronic State
Journal of Molecular Spectroscopy, 215 (1) :42-57
20021129.
Hirano, Tsuneo; Ishii, Keisaku; Odaka, Tina Erica; Jensen, Per
A Theoretical Study of MgNC and MgCN in the X~2Σ+ Electronic State
Journal of Molecular Spectroscopy, 215 (1) :42-57
20021128.
Jacob, Birgit; Partington, Jonathan R.; Pott, Sandra
Admissible and weakly admissible observation operators for the right shift semigroup
Proc. Edinb. Math. Soc. (2), 45 (2) :353--362
20021127.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
An ab initio study of the A\verb=~= \(^{2}\)\(\Pi\) state and the A\verb=~= \(^{2}\)\(\Pi\) ← X\verb=~= \(^{2}\)\(\Sigma\)\(^{+}\) electronic transition of MgNC
Journal of Molecular Spectroscopy, 211 (1) :147-161
20021126.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
An ab initio study of the A\verb=~= \(^{2}\)\(\Pi\) state and the A\verb=~= \(^{2}\)\(\Pi\) ← X\verb=~= \(^{2}\)\(\Sigma\)\(^{+}\) electronic transition of MgNC
Journal of Molecular Spectroscopy, 211 (1) :147-161
20021125.
Odaka, Tina Erica; Hirano, Tsuneo; Jensen, Per
An ab initio study of the A~ 2Π state and the A~ 2Π ← X~ 2Σ+ electronic transition of MgNC
Journal of Molecular Spectroscopy, 211 (1) :147-161
20021124.
Tausch, Michael W.; Weber, O.
Analytische Chemie - ein in der Schule verkannter Teilbereich?
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (4) :36
20021123.
Tausch, Michael W.
Aromatenchemie heute - Es muss nicht immer Benzol sein
Praxis der Naturwissenschaften - Chemie in der Schule, 51 (3) :1
20021122.
Geiger, Harald; Barnes, Ian; Becker, Karl Heinz; Bohn, Birger; Brauers, Theo; Donner, Birgit; Dorn, Hans-Peter; Elend, Manfred; Freitas Dinis, Carlos M.; Grossmann, Dirk; Hass, Heinz; Hein, Holger; Hoffmann, Axel; Hoppe, Lars; Hülsemann, Frank; Kley, Dieter; Klotz, Björn; Libuda, Hans G.; Maurer, Tobias; Mihelcic, Djuro; Moortgat, Geert K.; Olariu, Romeo; Neeb, Peter; Poppe, Dirk; Ruppert, Lars; Sauer, Claudia G.; Shestakov, Oleg; Somnitz, Holger; Stockwell, William R.; Thüner, Lars P.; Wahner, Andreas; Wiesen, Peter; Zabel, Friedhelm; Zellner, Reinhard; Zetzsch, Cornelius
Chemical Mechanism Development: Laboratory Studies and Model Applications
Tropospheric Chemistry
Seite 323-357
Herausgeber: Springer Netherlands, Dordrecht
2002
323-3571121.
Geiger, Harald; Barnes, Ian; Becker, Karl Heinz; Bohn, Birger; Brauers, Theo; Donner, Birgit; Dorn, Hans-Peter; Elend, Manfred; Freitas Dinis, Carlos M.; Grossmann, Dirk; Hass, Heinz; Hein, Holger; Hoffmann, Axel; Hoppe, Lars; H{ü}lsemann, Frank; Kley, Dieter; Klotz, Bj{ö}rn; Libuda, Hans G.; Maurer, Tobias; Mihelcic, Djuro; Moortgat, Geert K.; Olariu, Romeo; Neeb, Peter; Poppe, Dirk; Ruppert, Lars; Sauer, Claudia G.; Shestakov, Oleg; Somnitz, Holger; Stockwell, William R.; Th{ü}ner, Lars P.; Wahner, Andreas; Wiesen, Peter; Zabel, Friedhelm; Zellner, Reinhard; Zetzsch, Cornelius
Chemical Mechanism Development: Laboratory Studies and Model Applications
Tropospheric Chemistry
Seite 323-357
Herausgeber: Springer Netherlands, Dordrecht
2002
323-3571120.
Geiger, Harald; Barnes, Ian; Becker, Karl Heinz; Bohn, Birger; Brauers, Theo; Donner, Birgit; Dorn, Hans-Peter; Elend, Manfred; Freitas Dinis, Carlos M.; Grossmann, Dirk; Hass, Heinz; Hein, Holger; Hoffmann, Axel; Hoppe, Lars; H{ü}lsemann, Frank; Kley, Dieter; Klotz, Bj{ö}rn; Libuda, Hans G.; Maurer, Tobias; Mihelcic, Djuro; Moortgat, Geert K.; Olariu, Romeo; Neeb, Peter; Poppe, Dirk; Ruppert, Lars; Sauer, Claudia G.; Shestakov, Oleg; Somnitz, Holger; Stockwell, William R.; Th{ü}ner, Lars P.; Wahner, Andreas; Wiesen, Peter; Zabel, Friedhelm; Zellner, Reinhard; Zetzsch, Cornelius
Chemical Mechanism Development: Laboratory Studies and Model Applications
Tropospheric Chemistry
Seite 323-357
Herausgeber: Springer Netherlands, Dordrecht
2002
323-3571119.
Appel, Matthew F.; van der Veer, Wytze E.; Benter, Thorsten
Conductive carbon filled polymeric electrodes: Novel ion optical elements for time-of-flight mass spectrometers
Journal of The American Society for Mass Spectrometry, 13 (10) :1170-1175
2002
