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
- 2000
910.
Kleffmann, Jörg; Becker, Karl Heinz; Bröske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H2SO4/H2O and HNO3/H2SO4/H2O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000909.
Tausch, Michael W.
Stoffkreisläufe
Praxis der Naturwissenschaften - Chemie in der Schule, 49 (7) :1
2000908.
Bludsk{{\'y}}, Ota; Nachtigall, Petr; Hrus{{\'a}}k, Jan; Jensen, Per
The calculation of the vibrational states of SO\(_{2}\) in the C\verb=~= \(^{1}\)B\(_{2}\) electronic state up to the SO(\(^{3}\)\(\Sigma\)\(^{-}\))+O(\(^{3}\)P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000907.
Bludsk{{\'y}}, Ota; Nachtigall, Petr; Hrus{{\'a}}k, Jan; Jensen, Per
The calculation of the vibrational states of SO\(_{2}\) in the C\verb=~= \(^{1}\)B\(_{2}\) electronic state up to the SO(\(^{3}\)\(\Sigma\)\(^{-}\))+O(\(^{3}\)P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000906.
Bludský, Ota; Nachtigall, Petr; Hrusák, Jan; Jensen, Per
The calculation of the vibrational states of SO2 in the C~ 1B2 electronic state up to the SO(3Σ-)+O(3P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000905.
Denk, Georg; Günther, Michael
The influence of MOSFET model and network equations on circuit simulation
2000904.
Klamroth, Kathrin; Wiecek, Margaret M.
Time-dependent capital budgeting with multiple criteria
In Haimes, Y.Y. and Steuer, R.E., Editor, Research and Practice in Multiple Criteria Decision MakingBand487ausLecture Notes in Economics and Mathematical Systems, Seite 421-432
In Haimes, Y.Y. and Steuer, R.E., Editor
Herausgeber: Springer-Verlag
2000903.
East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; D{é}ch{{\`e}}ne, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S\(_{1}\)-S\(_{0}\) fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000902.
East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; D{é}ch{{\`e}}ne, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S\(_{1}\)-S\(_{0}\) fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000901.
East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; Déchène, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S1-S0 fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000900.
Denk, Georg; Feldmann, Uwe; Günther, Michael; Rentrop, Peter
Topics in Electric Circuit Simulation
2000899.
Tausch, Michael W.; Schmitz, R.-P.
Tropfsteinhöhlen und Kreislauf des Kohlenstoffdioxids in der Natur - eine Anwendung für Internet und CD-ROM
Praxis der Naturwissenschaften - Chemie in der Schule, 49 (7) :13
2000898.
Schandl, Bernd; Klamroth, Kathrin; Wiecek, Margaret M.
Using block norms in bicriteria optimization
In Haimes, Y.Y. and Steuer, R.E., Editor, Research and Practice in Multiple Criteria Decision MakingBand487ausLecture Notes in Economics and Mathematical Systems, Seite 149-160
In Haimes, Y.Y. and Steuer, R.E., Editor
Herausgeber: Springer-Verlag
2000897.
Brust, A. S.; Becker, Karl Heinz; Kleffmann, J{ö}rg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon896.
Brust, A. S.; Becker, Karl Heinz; Kleffmann, J{ö}rg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon895.
Brust, A. S.; Becker, Karl Heinz; Kleffmann, Jörg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon894.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Schwenke, D. W.; Jensen, Per; Cours, T.; Barbe, Alain; Jacon, M.
Variational EKE-calculations of rovibrational energies of the ozone molecule from an empirical potential function
Chemical Physics Letters, 316 (3-4) :271-279
2000893.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Schwenke, D. W.; Jensen, Per; Cours, T.; Barbe, Alain; Jacon, M.
Variational EKE-calculations of rovibrational energies of the ozone molecule from an empirical potential function
Chemical Physics Letters, 316 (3-4) :271-279
2000892.
Tyuterev, Vladimir G.; Tashkun, Sergey A.; Schwenke, D. W.; Jensen, Per; Cours, T.; Barbe, Alain; Jacon, M.
Variational EKE-calculations of rovibrational energies of the ozone molecule from an empirical potential function
Chemical Physics Letters, 316 (3-4) :271-279
2000891.
Schneider, Gisbert; Hilfiger, Laurence; Schneider, Petra; Kirsch, Stefan; Böhm, Hans-Joachim; Neidhart, Werner
Virtual Screening for Bioactive Molecules by Evolutionary De Novo Design
Angewandte Chemie, 39 (22) :4130–4133
2000
ISSN: 14337851, 15213773- 1999
890.
P. Schmitz, R.; Eisel, C.; Korn, S.; Tausch, Michael W.
''Chemie interaktiv'', Multimedia CD mit Lernsoftware für Schülerinnen und Schüler
Online
1999889.
Eisel, C.; Korn, S.; Schmitz, R.-P.; Tausch, Michael W.
''Duisburger Chemiedidaktik im WWW'' (Materialien für den Chemieunterricht, Präsentationen zu Vorträgen im Rahmen der Lehrerfortbildung u.a.)
Online
1999888.
Chudej, K.; Günther, M.
A global state space approach for the efficient numerical solution of state-constrained trajectory optimization problems
Journal of Optimization Theory and Applications, 103 (1) :75–93
1999
Herausgeber: Springer New York887.
Chudej, K.; G\"unther, Michael
A global state space approach for the efficient numerical solution of state-constrained trajectory optimization problems
J. Optim. Theory Appl., 103 (1) :75--93
1999886.
Geiger, Harald; Wiesen, Peter; Becker, Karl Heinz
A product study of the reaction of CH radicals with nitric oxide at 298 K
Physical Chemistry Chemical Physics, 1 (24) :5601-5606
1999
