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
1212.
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 & Francis1211.
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
20031210.
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 & Francis1209.
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.
Br{ö}ske, Rolf; Kleffmann, J{ö}rg; 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
20031206.
Br{ö}ske, Rolf; Kleffmann, J{ö}rg; 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.
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
20031204.
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 Press1203.
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 b1Σ+(b0+) → X3Σ-(X10+) transition of PI
Journal of Molecular Spectroscopy, 221 (1) :19-22
2003
Herausgeber: Academic Press1201.
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
191-1961200.
Kleffmann, J{ö}rg; 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
20031199.
Kleffmann, J{ö}rg; 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; 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
20031197.
Vogel, Bernhard; Vogel, Heike; Kleffmann, J{ö}rg; 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: Pergamon1196.
Vogel, Bernhard; Vogel, Heike; Kleffmann, J{ö}rg; 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: Pergamon1194.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and Discretization
, Modelling, Simulation and Optimization of Integrated Circuits: Proceedings of a Conference Held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001Band146, Seite 187
Springer Science \& Business Media
20031193.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, K. and {et al.}, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187--201
Birkhäuser Basel
In Antreich, K. and {et al.}, Editor
Herausgeber: Birkh\"auser Verlag, Basel
20031192.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187–201
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser, Basel
20031191.
Bartel, Andreas; Günther, Michael; Schulz, Martin
Modeling and discretization of a thermal-electric test circuit
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor, Modeling, Simulation, and Optimization of Integrated Circuits: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, November 25-December 1, 2001, Seite 187–201
In Antreich, Kurt and Bulirsch, Roland and Gilg, Albert and Rentrop, Peter, Editor
Herausgeber: Birkhäuser, Basel
20031190.
Farkas, Bálint
On the duals of L\sb p spaces with 0<p<1
Acta Math. Hungar., 98 (1-2) :71-77
20031189.
Bátkai, András; Farkas, Bálint
On the effect of small delays to the stability of feedback systems
, Evolution equations: applications to physics, industry, life sciences and economics (<prt>L</prt>evico <prt>T</prt>erme, 2000) Band 55 aus Progr. Nonlinear Differential Equations Appl.
Seite 83-94
Herausgeber: Birkhäuser, Basel
2003
83-941188.
Vogt, Rainer; Scheer, Volker; Casati, Roberto; Benter, Thorsten
On-Road Measurement of Particle Emission in the Exhaust Plume of a Diesel Passenger Car
Environmental Science \& Technology, 37 (18) :4070-4076
2003
