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

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; 57.
Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982
DOI: 10.1016/0022-2860(82)87210-4; 56.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ emissions from group V-VII diatomic molecules: b0+ → X10+, X20+ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982
DOI: 10.1016/0009-2614(82)83223-5; 55.
Tausch, Michael W.
Modelle im Chemieunterricht
Der mathematische und naturwissenschaftliche Unterricht (MNU), 35 :226
1982; 54.
Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982
DOI: 10.1016/0009-2614(82)83326-5; 53.
Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C\(_{2}\)O radicals in the C\(_{3}\)O\(_{2}\) + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982
DOI: 10.1016/0009-2614(82)83326-5; 52.
Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C2O radicals in the C3O2 + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982
DOI: 10.1016/0009-2614(82)83326-5; 51.
Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982
DOI: 10.1002/jrs.1250120318; 50.
Jensen, Per; Brodersen, Svend
The \(\nu\)\(_{5}\) Raman band of CH\(_{3}\)CD\(_{3}\)
Journal of Raman Spectroscopy, 12 (3) :295-299
1982
DOI: 10.1002/jrs.1250120318; 49.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982
DOI: 10.1063/1.443785; 48.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH\(_{2}\) in the X\verb=~=\(^{3}\)B\(_{1}\) ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982
DOI: 10.1063/1.443785; 47.
Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH2 in the X~3B1 ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982
DOI: 10.1063/1.443785; 46.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982
DOI: 10.1016/0022-2852(82)90298-3; 45.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982
DOI: 10.1016/0022-2852(82)90298-3; 44.
Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982
DOI: 10.1016/0022-2852(82)90298-3; 43.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A\verb=~=\(^{1}\)A\(_{2}\) and a\verb=~=\(^{3}\)A\(_{2}\) electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
1982
DOI: 10.1016/0022-2852(82)90241-7; 42.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A\verb=~=\(^{1}\)A\(_{2}\) and a\verb=~=\(^{3}\)A\(_{2}\) electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
1982
DOI: 10.1016/0022-2852(82)90241-7; 41.
Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A~1A2 and a~3A2 electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
1982
DOI: 10.1016/0022-2852(82)90241-7; 40.
Jensen, Per; Brodersen, Svend
The ν5 Raman band of CH3CD3
Journal of Raman Spectroscopy, 12 (3) :295-299
1982
DOI: 10.1002/jrs.1250120318

Index Analysis

Group members working on that field

Cooperations

Publications

64.

63.

62.

61.

60.

59.

58.

57.

56.

55.

54.

53.

52.

51.

50.

49.

48.

47.

46.

45.

44.

43.

42.

41.

40.