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



1988

230.

Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v'=0,1,2) - rates and channels of energy transfer and quenching
Chemical Physics, 122 (3) :463-470
1988

229.

Wildt, J{ü}rgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of O\(_{2}\)(b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\), v'=0,1,2) - rates and channels of energy transfer and quenching
Chemical Physics, 122 (3) :463-470
1988

228.

Czech, C. M.; Kling, H.-W.; Hartkamp, H.
Kontinuierliche Derivatisierung von schwerflüchtigen Wasserinhaltsstoffen durch Periodat-Oxidation in Verbindung mit dem Contistrip-Verfahren
Fresenius' Journal of Analytical Chemistry, 332 (4) :341--344
1988

227.

Jensen, Per
Hamiltonians for the internal dynamics of triatomic molecules
Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics, 84 (9) :1315-1339
1988

226.

Jensen, Per
Hamiltonians for the internal dynamics of triatomic molecules
Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics, 84 (9) :1315-1339
1988

225.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

224.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO3 radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

223.

[german] Tausch, Michael W.; Paterkiewicz, D.
Fluoreszenz und Phosphoreszenz
Praxis der Naturwissenschaften (Chemie), 36 :14
1988

222.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

221.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

220.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

219.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC+ and C3 using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

218.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

217.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

216.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO3 and the Determination of Absolute Rate Constants for the Reaction of the NO3 Radical with CH3SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

215.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

214.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

213.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO\(_{3}\) radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

212.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

211.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

210.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC+ and CCN+
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

209.

Jensen, Per
A variational calculation of the rotation-vibration energies for H\(_{2}\)O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

208.

Jensen, Per
A variational calculation of the rotation-vibration energies for H\(_{2}\)O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

207.

Jensen, Per
A variational calculation of the rotation-vibration energies for H2O from Ab initio data
Journal of Molecular Structure, 190 :149-161
1988

206.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO\(_{3}\) radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

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