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

1983: 82.
Wildt, J{ü}rgen; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative lifetime and quenching of SO(b\(^{1}\)\(\Sigma\)\(^{+}\),\(\nu\)'=0)
Chemical Physics, 80 (1-2) :167-175
1983
DOI: 10.1016/0301-0104(83)85177-5; 81.
Wildt, Jürgen; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative lifetime and quenching of SO(b1Σ+,ν'=0)
Chemical Physics, 80 (1-2) :167-175
1983
DOI: 10.1016/0301-0104(83)85177-5; 80.
Wildt, J{ü}rgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b\(^{1}\)\(\Sigma\) states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
1983; 79.
Wildt, J{ü}rgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b\(^{1}\)\(\Sigma\) states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
1983; 78.
Wildt, Jürgen; Bielefeld, M.; Fink, Ewald H.; Winter, R.; Zabel, Friedhelm
Radiative livetimes of the metastable b1Σ states of SO, SeO, PCl and PBr
Bulletin des Sociétés Chimiques Belges, 92 (6-7) :523-524
1983; 77.
[german] Tausch, Michael W.
Strukturaufklärung in der organischen Chemie - Ermittlung der Strukturformeln von Maleinsäure und Fumarsäure
Praxis der Naturwissenschaften (Chemie), 32 :44
1983; 76.
Holstein, K. J.; Fink, Ewald H.; Zabel, Friedhelm
The \(\nu\)\(_{3}\) vibration of electronically excited HO\(_{2}\)(A\(^{2}\)A')
Journal of Molecular Spectroscopy, 99 (1) :231-234
1983
DOI: 10.1016/0022-2852(83)90307-7; 75.
Holstein, K. J.; Fink, Ewald H.; Zabel, Friedhelm
The \(\nu\)\(_{3}\) vibration of electronically excited HO\(_{2}\)(A\(^{2}\)A')
Journal of Molecular Spectroscopy, 99 (1) :231-234
1983
DOI: 10.1016/0022-2852(83)90307-7; 74.
Jensen, Per; Bunker, Philip R.
The application of the nonrigid bender Hamiltonian to a quasilinear molecule
Journal of Molecular Spectroscopy, 99 (2) :348-356
1983
DOI: 10.1016/0022-2852(83)90319-3; 73.
Jensen, Per; Bunker, Philip R.
The application of the nonrigid bender Hamiltonian to a quasilinear molecule
Journal of Molecular Spectroscopy, 99 (2) :348-356
1983
DOI: 10.1016/0022-2852(83)90319-3; 72.
Jensen, Per; Bunker, Philip R.
The application of the nonrigid bender Hamiltonian to a quasilinear molecule
Journal of Molecular Spectroscopy, 99 (2) :348-356
1983
DOI: 10.1016/0022-2852(83)90319-3; 71.
Winnewisser, Brenda P.; Jensen, Per
The infrared spectrum of fulminic acid, HCNO, in the \(\nu\)\(_{4}\) fundamental region
Journal of Molecular Spectroscopy, 101 (2) :408-421
1983
DOI: 10.1016/0022-2852(83)90145-5; 70.
Winnewisser, Brenda P.; Jensen, Per
The infrared spectrum of fulminic acid, HCNO, in the \(\nu\)\(_{4}\) fundamental region
Journal of Molecular Spectroscopy, 101 (2) :408-421
1983
DOI: 10.1016/0022-2852(83)90145-5; 69.
Winnewisser, Brenda P.; Jensen, Per
The infrared spectrum of fulminic acid, HCNO, in the ν4 fundamental region
Journal of Molecular Spectroscopy, 101 (2) :408-421
1983
DOI: 10.1016/0022-2852(83)90145-5; 68.
Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983
DOI: 10.1016/0167-7977(83)90003-5; 67.
Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983
DOI: 10.1016/0167-7977(83)90003-5; 66.
Jensen, Per
The nonrigid bender Hamiltonian for calculating the rotation-vibration energy levels of a triatomic molecule
Computer Physics Reports, 1 (1) :1-55
1983
DOI: 10.1016/0167-7977(83)90003-5; 65.
Holstein, K. J.; Fink, Ewald H.; Zabel, Friedhelm
The ν3 vibration of electronically excited HO2(A2A')
Journal of Molecular Spectroscopy, 99 (1) :231-234
1983
DOI: 10.1016/0022-2852(83)90307-7
1982: 64.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules b0\(_{g}\)\(^{+}\) → X\(^{2}\)1\(_{g}\) emissions of Se\(_{2}\) and Te\(_{2}\)
Chemical Physics Letters, 86 (2) :118-122
1982
DOI: 10.1016/0009-2614(82)83252-1; 63.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules b0\(_{g}\)\(^{+}\) → X\(^{2}\)1\(_{g}\) emissions of Se\(_{2}\) and Te\(_{2}\)
Chemical Physics Letters, 86 (2) :118-122
1982
DOI: 10.1016/0009-2614(82)83252-1; 62.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982
DOI: 10.1016/0022-2860(82)87210-4; 61.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) and a\(^{1}\)\(\Delta\) emissions from group VI-VI diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)1 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982
DOI: 10.1016/0022-2860(82)87210-4; 60.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)0\(^{+}\) emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982
DOI: 10.1016/0009-2614(82)83223-5; 59.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b\(^{1}\)\(\Sigma\)\(^{+}\) emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\), X\(_{2}\)0\(^{+}\) emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982
DOI: 10.1016/0009-2614(82)83223-5; 58.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules b0g+ → X21g emissions of Se2 and Te2
Chemical Physics Letters, 86 (2) :118-122
1982
DOI: 10.1016/0009-2614(82)83252-1

Index Analysis

Group members working on that field

Cooperations

Publications

82.

81.

80.

79.

78.

77.

76.

75.

74.

73.

72.

71.

70.

69.

68.

67.

66.

65.

64.

63.

62.

61.

60.

59.

58.