Applied and Computational Mathematics (ACM)

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

542.

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.

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 Press

DOI: 10.1006/jmsp.1994.1277

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 Press

DOI: 10.1006/jmsp.1994.1277

539.

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 Press

DOI: 10.1006/jmsp.1994.1277

538.

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
1994

DOI: 10.1063/1.468258

537.

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
1994

DOI: 10.1063/1.468258

536.

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
1994

DOI: 10.1063/1.468258

535.

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, Canada

DOI: 10.1139/p94-114

534.

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, Canada

DOI: 10.1139/p94-114

533.

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, Canada

DOI: 10.1139/p94-114

532.

Tausch, Michael W.
Atom, Molekül, Mol - eine Schulbuchsynopse über 80 Jahre
Praxis der Naturwissenschaften (Chemie), 43 (7) :32
1994

531.

Günther, M.
Charge-oriented modelling of electric circuits and Rosenbrock-Wanner methods
Journal of Computing and Information, 4 :41–53
1994

530.

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
1994

DOI: 10.1063/1.467329

529.

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
1994

DOI: 10.1063/1.467329

528.

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
1994

DOI: 10.1063/1.467329

527.

Denk, Georg; Selting, Petra A
Efficient numerical methods in electronic circuit simulation
Report TUM-M9413
1994
Herausgeber: Technische Universität München

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526.

Denk, Georg; Selting, Petra A
Efficient numerical methods in electronic circuit simulation
1994

525.

Tausch, Michael W.; Wambach, H.
Entropie - was ist wissenschaftlich vertretbar und didaktisch sinnvoll?
Praxis der Naturwissenschaften (Chemie), 43 (2) :35
1994

524.

Skov, H.; Benter, Thorsten; Schindler, Ralph N.; Hjorth, J.; Restelli, G.
Epoxide formation in the reactions of the nitrate radical with 2,3-dimethyl-2-butene, cis- and trans-2-butene and isoprene
Atmospheric Environment, 28 (9) :1583-1592
1994

DOI: 10.1016/1352-2310(94)90304-2

523.

Skov, H.; Benter, Thorsten; Schindler, Ralph N.; Hjorth, J.; Restelli, G.
Epoxide formation in the reactions of the nitrate radical with 2,3-dimethyl-2-butene, cis- and trans-2-butene and isoprene
Atmospheric Environment, 28 (9) :1583-1592
1994

DOI: 10.1016/1352-2310(94)90304-2

522.

Skov, H.; Benter, Thorsten; Schindler, Ralph N.; Hjorth, J.; Restelli, G.
Epoxide formation in the reactions of the nitrate radical with 2,3-dimethyl-2-butene, cis- and trans-2-butene and isoprene
Atmospheric Environment, 28 (9) :1583-1592
1994

DOI: 10.1016/1352-2310(94)90304-2

521.

Kozin, Igor N.; Jensen, Per
Fourfold clusters of rovibrational energy levels for H\(_{2}\)S studied with a potential energy surface derived from experiment
Journal of Molecular Spectroscopy, 163 (2) :483-509
1994
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1994.1041

520.

Kozin, Igor N.; Jensen, Per
Fourfold clusters of rovibrational energy levels for H\(_{2}\)S studied with a potential energy surface derived from experiment
Journal of Molecular Spectroscopy, 163 (2) :483-509
1994
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1994.1041

519.

Kozin, Igor N.; Jensen, Per
Fourfold clusters of rovibrational energy levels for H2S studied with a potential energy surface derived from experiment
Journal of Molecular Spectroscopy, 163 (2) :483-509
1994
Herausgeber: Academic Press

DOI: 10.1006/jmsp.1994.1041

518.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Zhu, Q.-S.
High-resolution study of the emission system of \(^{80}\)Se\(_{2}\) in the near infrared
Canadian Journal of Physics, 72 (11-12) :919-924
1994
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p94-121