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

239.

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

DOI: 10.1016/0022-2852(88)90164-6

238.

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

DOI: 10.1016/0022-2852(88)90164-6

237.

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

DOI: 10.1016/0022-2852(88)90164-6

236.

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

DOI: 10.1016/0022-2852(88)90271-8

235.

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

DOI: 10.1016/0022-2852(88)90271-8

234.

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

DOI: 10.1016/0022-2852(88)90271-8

233.

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

DOI: 10.1016/0022-2860(88)80280-1

232.

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

DOI: 10.1016/0022-2860(88)80280-1

231.

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

DOI: 10.1016/0022-2860(88)80280-1

230.

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

DOI: 10.1016/0009-2614(88)85134-0

229.

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

DOI: 10.1016/0009-2614(88)85134-0

228.

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

DOI: 10.1016/0009-2614(88)85134-0

227.

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

DOI: 10.1016/0022-2852(88)90338-4

226.

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

DOI: 10.1016/0022-2852(88)90338-4

225.

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

DOI: 10.1016/0022-2852(88)90338-4

224.

Heilmann, Margareta
Commutativity of operators from Baskakov-Durrmeyer type
Constructive Theory of Functions - Proceedings of the International Conference, Varna, Bulgaria, 1987, Seite 197-206
1988

223.

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

222.

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

DOI: 10.1039/F29888401315

221.

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

DOI: 10.1039/F29888401315

220.

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

DOI: 10.1039/F29888401315

219.

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

218.

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

DOI: 10.1016/0301-0104(88)80027-2

217.

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

DOI: 10.1016/0301-0104(88)80027-2

216.

Wildt, Jürgen; Bednarek, G.; Fink, Ewald H.; Wayne, Richard P.
Laser excitation of O2(b1Σg+, v'=0,1,2) - rates and channels of energy transfer and quenching
Chemical Physics, 122 (3) :463-470
1988

DOI: 10.1016/0301-0104(88)80027-2

215.

Heilmann, Margareta
Lp-saturation of some modified Bernstein operators
Journal of Approximation Theory, 54 (3) :260-273
1988
ISSN: 0021-9045

DOI: 10.1016/0021-9045(88)90003-2