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

1989

267.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.
Near-infrared emission bands of TeH and TeD
Journal of Molecular Spectroscopy, 138 (1) :19-28
1989

DOI: 10.1016/0022-2852(89)90094-5

266.

Heilmann, Margareta
On simultaneous approximation by optimal algebraic polynomials
Results in Mathematics, 16 (1-2) :77-81
1989

DOI: 10.1007/BF03322645

265.

Heilmann, Margareta; Müller, Manfred
On simultaneous approximation by the method of Baskakov-Durrmeyer operators
Numerical Functional Analysis and Optimization, 10 (1-2) :127-138
1989

DOI: 10.1080/01630568908816295

264.

[german] Tausch, Michael W.; Wöhrle, D.
Photokatalyse
Praxis der Naturwissenschaften (Chemie), 38 :37
1989

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263.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X\(^{2}\)\(\Pi\)) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

262.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X\(^{2}\)\(\Pi\)) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

261.

Becker, Karl Heinz; Engelhardt, B.; Wiesen, Peter; Bayes, Kyle D.
Rate constants for CH(X2Π) reactions at low total pressures
Chemical Physics Letters, 154 (4) :342-348
1989

DOI: 10.1016/0009-2614(89)85367-9

260.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0\(^{+}\) → X\(_{1}\)0\(^{+}\) system of \(^{130}\)Te\(^{80}\)Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

259.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0\(^{+}\) → X\(_{1}\)0\(^{+}\) system of \(^{130}\)Te\(^{80}\)Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

258.

Fink, Ewald H.; Setzer, Klaus-Dieter; Ramsay, D. A.; Vervloet, M.; Xu, G. Z.
Rotational analysis of the 0-0 band of the b0+ → X10+ system of 130Te80Se
Journal of Molecular Spectroscopy, 136 (1) :218-221
1989

DOI: 10.1016/0022-2852(89)90236-1

257.

Tausch, Michael W.; Wachtendonk, M.
STOFF-FORMEL-UMWELT, BAND 1: CHEMISCHE GLEICHGEWICHTE - ELEKTROCHEMIE, Lehrbuch für die S II (Grund- und Leistungskurse), 172 Seiten
Herausgeber: C. C. Buchner, Bamberg
1989

256.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

255.

Wildt, J{ü}rgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

254.

Wildt, Jürgen; Fink, Ewald H.; Biggs, P.; Wayne, Richard P.
The collision-induced radiation of O2(a1Δg)
Chemical Physics, 139 (2-3) :401-407
1989

DOI: 10.1016/0301-0104(89)80152-1

253.

Jensen, Per
The potential energy surface for the C\(_{3}\) molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

252.

Jensen, Per
The potential energy surface for the C\(_{3}\) molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

251.

Jensen, Per
The potential energy surface for the C3 molecule determined from experimental data. Evidence for a bent equilibrium structure
Collection of Czechoslovak Chemical Communications, 54 (5) :1209-1218
1989
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19891209

250.

Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989

DOI: 10.1016/0022-2852(89)90203-8

249.

Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989

DOI: 10.1016/0022-2852(89)90203-8

248.

Jensen, Per
The potential energy surface for the electronic ground state of the water molecule determined from experimental data using a variational approach
Journal of Molecular Spectroscopy, 133 (2) :438-460
1989

DOI: 10.1016/0022-2852(89)90203-8

247.

Schönfeld, J; Loennecken, I; Gückel, C
Unilateral pulsating tinnitus: paraganglioma of the glomus jugulare with predominantly vascular extension
Medizinische Klinik (Munich, Germany: 1983), 84 (9) :445--449
1989

246.

Heilmann, Margareta; Müller, Manfred
Weighted simultaneous L_p-approximation by the method of Baskakov-Durrmeyer operators
Approximation Theory VI, Proc. 6th Int. Symp., College Station/TX USA1989Band 1, Seite 331-332
1989

DOI: 10.1007/s10474-011-0135-x

1988

245.

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

DOI: 10.1016/0022-2852(88)90268-8

244.

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

DOI: 10.1016/0022-2852(88)90268-8

243.

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

DOI: 10.1016/0022-2852(88)90268-8