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
- 2003
1219.
Ali, G; Bartel, A; Tischendorf, C
Elliptic partial differential-algebraic multiphysics models in electrical network design
Mathematical Models and Methods in Applied Sciences, 13 (09) :1261--1278
2003
Herausgeber: World Scientific1218.
Alì, Giuseppe; Bartel, Andreas; Günther, Michael; Tischendorf, Caren
Elliptic partial differential-algebraic multiphysics models in electrical network design
Mathematical Models and Methods in Applied Sciences, 13 (09) :1261–1278
2003
Herausgeber: World Scientific Publishing1217.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Das, K. K.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and theoretical study of the electronic states and spectra of PbLi
Journal of Molecular Spectroscopy, 217 (1) :127-141
2003
Herausgeber: Academic Press1216.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Das, K. K.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and theoretical study of the electronic states and spectra of PbLi
Journal of Molecular Spectroscopy, 217 (1) :127-141
2003
Herausgeber: Academic Press1215.
Setzer, Klaus-Dieter; Borkowska-Burnecka, J.; Zyrnicki, W.; Pravilov, A. M.; Fink, Ewald H.; Das, K. K.; Liebermann, Heinz-Peter; Alekseyev, Aleksey B.; Buenker, Robert J.
Experimental and theoretical study of the electronic states and spectra of PbLi
Journal of Molecular Spectroscopy, 217 (1) :127-141
2003
Herausgeber: Academic Press1214.
Günther, Michael; Jüngel, Ansgar
Finanzderivate mit MATLAB{\textregistered}
20031213.
Bartel, A.:
First order thermal {PDAE} models in electric circuit design
In Troch, I. and Breitenecker, F., Editor, Proceedings 4th Mathmod, Vienna 2003
In Troch, I. and Breitenecker, F., Editor
20031212.
Bartel, Andreas
First order thermal PDAE models in electric circuit design
In Troch, Inge and Breitenecke, F., Editor, 4th MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingausArgesim Report 24, Seite 1376–1381
In Troch, Inge and Breitenecke, F., Editor
Herausgeber: TU Wien
20031211.
Bartel, Andreas; Günther, Michael
From {SOI} to abstract electric-thermal-{1D} multiscale modeling for first order thermal effects
Mathematical and Computer Modelling of Dynamical Systems, 9 (1) :25--44
2003
Herausgeber: Taylor & Francis1210.
Bartel, A.; G\"unther, Michael
From {SOI} to abstract electric-thermal-1D mutiscale modeling for first order thermal effects
Mathematical and Computer Modelling of Dynamical Systems, 9 :25--44
20031209.
Bartel, Andreas; Günther, Michael
From SOI to abstract electric-thermal-1D multiscale modeling for first order thermal effects
Mathematical and Computer Modelling of Dynamical Systems, 9 (1) :25–44
2003
Herausgeber: Taylor & Francis1208.
Bartel, Andreas; Günther, Michael
From SOI to abstract electric-thermal-1D multiscale modeling for first order thermal effects
Mathematical and Computer Modelling of Dynamical Systems, 9 (1) :25--44
2003
Herausgeber: Taylor \& Francis1207.
Bartel, Andreas; Günther, Michael
From SOI to abstract electric-thermal-1D multiscale modeling for first order thermal effects
Mathematical and Computer Modelling of Dynamical Systems, 9 (1) :25–44
2003
Herausgeber: Taylor & Francis1206.
Br{ö}ske, Rolf; Kleffmann, Jörg; Wiesen, Peter
Heterogeneous conversion of NO\(_{2}\) on secondary organic aerosol surfaces: A possible source of nitrous acid (HONO) in the atmosphere?
Atmospheric Chemistry and Physics, 3 (3) :469-474
20031205.
Br{ö}ske, Rolf; Kleffmann, Jörg; Wiesen, Peter
Heterogeneous conversion of NO\(_{2}\) on secondary organic aerosol surfaces: A possible source of nitrous acid (HONO) in the atmosphere?
Atmospheric Chemistry and Physics, 3 (3) :469-474
20031204.
Bröske, Rolf; Kleffmann, Jörg; Wiesen, Peter
Heterogeneous conversion of NO2 on secondary organic aerosol surfaces: A possible source of nitrous acid (HONO) in the atmosphere?
Atmospheric Chemistry and Physics, 3 (3) :469-474
20031203.
Setzer, Klaus-Dieter; Beutel, M.; Fink, Ewald H.
High-resolution study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\)) transition of PI
Journal of Molecular Spectroscopy, 221 (1) :19-22
2003
Herausgeber: Academic Press1202.
Setzer, Klaus-Dieter; Beutel, M.; Fink, Ewald H.
High-resolution study of the b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\)) transition of PI
Journal of Molecular Spectroscopy, 221 (1) :19-22
2003
Herausgeber: Academic Press1201.
Setzer, Klaus-Dieter; Beutel, M.; Fink, Ewald H.
High-resolution study of the b1Σ+(b0+) → X3Σ-(X10+) transition of PI
Journal of Molecular Spectroscopy, 221 (1) :19-22
2003
Herausgeber: Academic Press1200.
Rommes, J.; Vorst, H. A.; Maten, E. J. W.
Jacobi-Davidson Methods and Preconditioning with Applications in Pole-zero Analysis
In A. Buikis and R. Ciegis and A. D. Fitt, Editor, Progress in Industrial Mathematics at ECMI 2002, Jurmala Band 5 aus Mathematics in Industry
Seite 191-196
Herausgeber: Springer Berlin Heidelberg
2003
191-1961199.
Kleffmann, Jörg; Kurtenbach, Ralf; L{ö}rzer, Jutta C.; Wiesen, Peter; Kalthoff, Norbert; Vogel, Bernhard; Vogel, Heike
Measured and simulated vertical profiles of nitrous acid - Part I: Field measurements
Atmospheric Environment, 37 (21) :2949-2955
20031198.
Kleffmann, Jörg; Kurtenbach, Ralf; L{ö}rzer, Jutta C.; Wiesen, Peter; Kalthoff, Norbert; Vogel, Bernhard; Vogel, Heike
Measured and simulated vertical profiles of nitrous acid - Part I: Field measurements
Atmospheric Environment, 37 (21) :2949-2955
20031197.
Kleffmann, Jörg; Kurtenbach, Ralf; Lörzer, Jutta C.; Wiesen, Peter; Kalthoff, Norbert; Vogel, Bernhard; Vogel, Heike
Measured and simulated vertical profiles of nitrous acid - Part I: Field measurements
Atmospheric Environment, 37 (21) :2949-2955
20031196.
Vogel, Bernhard; Vogel, Heike; Kleffmann, Jörg; Kurtenbach, Ralf
Measured and simulated vertical profiles of nitrous acid - Part II. Model simulations and indications for a photolytic source
Atmospheric Environment, 37 (21) :2957-2966
2003
Herausgeber: Pergamon1195.
Vogel, Bernhard; Vogel, Heike; Kleffmann, Jörg; Kurtenbach, Ralf
Measured and simulated vertical profiles of nitrous acid - Part II. Model simulations and indications for a photolytic source
Atmospheric Environment, 37 (21) :2957-2966
2003
Herausgeber: Pergamon
