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
- 1995
550.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS\(_{2}\) Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press549.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS\(_{2}\) Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press548.
Kolbuszewski, M.; Bunker, Philip R.; Jensen, Per
The Potential Energy Function of CS2 Derived from Rovibrational Data
Journal of Molecular Spectroscopy, 170 (1) :158-165
1995
Herausgeber: Academic Press547.
Denk, Georg; Feldmann, Uwe; Günther, Michael; Rentrop, Peter
Topics in electric circuit simulation
Preprint (1740)
1995
Herausgeber: Technische Hochschule Darmstadt546.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH\(_{3}\)OBr; Br(\(^{2}\)P\(_{3/2}\)) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995545.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH\(_{3}\)OBr; Br(\(^{2}\)P\(_{3/2}\)) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995544.
Benter, Thorsten; Feldmann, Ch R.; Kirchner, Ulf; Schmidt, M.; Schmidt, Sven; Schindler, Ralph N.
UV/VIS-absorption Spectra of HOBr and CH3OBr; Br(2P3/2) Atom Yields in the Photolysis of HOBr
Berichte der Bunsengesellschaft für physikalische Chemie, 99 (9) :1144-1147
1995543.
Günther, M.; Lehn, J.; Rentrop, P.; Rettig, S.; Simeon, B.
Wissenschaftliches Rechnen aus der Sicht der Mathematik
Thema Forschung 2/95, 2 :26–35
1995
Herausgeber: Technische Hochschule Darmstadt542.
G\"unther, Michael; Lehn, J.; Rentrop, P.; Rettig, S.; Simeon, B.
Wissenschaftliches Rechnen aus der Sicht der Mathematik
Thema Forschung 2/95, TH Darmstadt, 2 :26--35
1995- 1994
541.
Heynderickx, I. E. J.; Potze, W.; Maten, E. J. W.Ter
Influence of a temperature gradient on the simple shear now of a nematic liquid crystal
Journal of Non-Newtonian Fluid Mechanics, 55 (2) :137--161
November 1994
Herausgeber: Elsevier {BV}540.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press539.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press538.
Jensen, Per; Tashkun, Sergey A.; Tyuterev, Vladimir G.
A Refined Potential Energy Surface for the Electronic Ground State of the Water Molecule
Journal of Molecular Spectroscopy, 168 (2) :271-289
1994
Herausgeber: Academic Press537.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
A spectroscopically determined potential energy surface for the ground state of H\(_{2}\)\(^{16}\)O: A new level of accuracy
The Journal of Chemical Physics, 101 (9) :7651-7657
1994536.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
A spectroscopically determined potential energy surface for the ground state of H\(_{2}\)\(^{16}\)O: A new level of accuracy
The Journal of Chemical Physics, 101 (9) :7651-7657
1994535.
Polyansky, Oleg L.; Jensen, Per; Tennyson, Jonathan
A spectroscopically determined potential energy surface for the ground state of H216O: A new level of accuracy
The Journal of Chemical Physics, 101 (9) :7651-7657
1994534.
Kraemer, Wolfgang P.; Jensen, Per; Bunker, Philip R.
An ab initio calculation of the vibronic energies of the CH\(_{2}\)\(^{+}\) molecule
Canadian Journal of Physics, 72 (11-12) :871-878
1994
Herausgeber: NRC Research Press Ottawa, Canada533.
Kraemer, Wolfgang P.; Jensen, Per; Bunker, Philip R.
An ab initio calculation of the vibronic energies of the CH\(_{2}\)\(^{+}\) molecule
Canadian Journal of Physics, 72 (11-12) :871-878
1994
Herausgeber: NRC Research Press Ottawa, Canada532.
Kraemer, Wolfgang P.; Jensen, Per; Bunker, Philip R.
An ab initio calculation of the vibronic energies of the CH2+ molecule
Canadian Journal of Physics, 72 (11-12) :871-878
1994
Herausgeber: NRC Research Press Ottawa, Canada531.
Tausch, Michael W.
Atom, Molekül, Mol - eine Schulbuchsynopse über 80 Jahre
Praxis der Naturwissenschaften (Chemie), 43 (7) :32
1994530.
Günther, M.
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Journal of Computing and Information, 4 :41–53
1994529.
Alml{ö}f, Jan; Jensen, Per; Northrup, F. J.; Rohlfing, Celeste Michael; Rohlfing, E. A.; Sears, T. J.
Comment on ''The \(\nu\)\(_{1}\) + \(\nu\)\(_{3}\) combination mode of C\(_{3}\) in Ar and Kr matrices: Evidence for a bent structure'' [J. Chem. Phys. 99, 7371 (1993)]
The Journal of Chemical Physics, 101 (6) :5413-5413
1994528.
Alml{ö}f, Jan; Jensen, Per; Northrup, F. J.; Rohlfing, Celeste Michael; Rohlfing, E. A.; Sears, T. J.
Comment on ''The \(\nu\)\(_{1}\) + \(\nu\)\(_{3}\) combination mode of C\(_{3}\) in Ar and Kr matrices: Evidence for a bent structure'' [J. Chem. Phys. 99, 7371 (1993)]
The Journal of Chemical Physics, 101 (6) :5413-5413
1994527.
Almlöf, Jan; Jensen, Per; Northrup, F. J.; Rohlfing, Celeste Michael; Rohlfing, E. A.; Sears, T. J.
Comment on "The ν1 + ν3 combination mode of C3 in Ar and Kr matrices: Evidence for a bent structure" [J. Chem. Phys. 99, 7371 (1993)]
The Journal of Chemical Physics, 101 (6) :5413-5413
1994526.
Denk, Georg; Selting, Petra A
Efficient numerical methods in electronic circuit simulation
Report TUM-M9413
1994
Herausgeber: Technische Universität München
