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
- 1984
117.
Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 band systems of AsCl and AsBr
Chemical Physics Letters, 111 (1-2) :100-104
1984116.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ Emissions from group V-VII diatomic molecules. b0+ → X10+, X21 emissions of AsI and SbI
Chemical Physics Letters, 104 (4) :383-388
1984115.
Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984114.
Jensen, Per
C\(_{3}\)O\(_{2}\) as a semirigid bender: The degenerate \(\nu\)\(_{5}\) state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984113.
Jensen, Per
C3O2 as a semirigid bender: The degenerate ν5 state
Journal of Molecular Spectroscopy, 104 (1) :59-71
1984112.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984111.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH\(_{3}\)NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984110.
Kreglewski, Marek; Jensen, Per
Determination of the skeletal bending potential function for SiH3NCO from the microwave spectrum
Journal of Molecular Spectroscopy, 103 (2) :312-320
1984109.
Glöckner, W.; Tausch, Michael W.; Autorenteam
MATERIALIEN FÜR DER KURSUNTERRICHT CHEMIE, Aufgabensammlung mit Klausur- und Abituraufgaben aus allen Bereichen der Schulchemie, 3 Bände
Herausgeber: Aulis Deubner\&Co KG, Köln
1984108.
Winkler, R.
Numerische Behandlung von parameterabhängigen Zwei-Punkt-Randwertaufgaben unter Berücksichtigung von Verzweigungsproblemen
Humboldt-Universität zu Berlin
1984107.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984106.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))-sensitized chemiluminescence of a\(^{1}\)\(\Delta\) → X\(^{3}\)\(\Sigma\)\(^{-}\) and b\(^{1}\)\(\Sigma\)\(^{+}\) → X\(^{3}\)\(\Sigma\)\(^{-}\) transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984105.
Bielefeld, M.; Elfers, G.; Fink, Ewald H.; Kruse, H.; Wildt, Jürgen; Winter, R.; Zabel, Friedhelm
O2(a1Δg)-sensitized chemiluminescence of a1Δ → X3Σ- and b1Σ+ → X3Σ- transitions of group VI-group VI and group V-group VII diatomic molecules
Journal of Photochemistry, 25 (2-4) :419-438
1984104.
Maten, E. J. W.
Stability analysis of finite difference methods for fourth order parabolic partial differential equations
Rijksuniversiteit Utrecht
1984103.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH\(_{2}\)N\(_{2}\) in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984102.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH\(_{2}\)N\(_{2}\) in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984101.
Becker, Karl Heinz; Horie, O.; Wiesen, Peter
The formation of CH radicals during the photolysis of CH2N2 in the presence of hydrogen and oxygen atoms
Journal of Photochemistry, 24 (3) :293-297
1984- 1983
100.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=\(^{3}\)B\(_{1}\) electronic state of methylene CH\(_{2}\)
The Journal of Chemical Physics, 79 (3) :1224-1228
198399.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=\(^{3}\)B\(_{1}\) electronic state of methylene CH\(_{2}\)
The Journal of Chemical Physics, 79 (3) :1224-1228
198398.
Bunker, Philip R.; Jensen, Per
A refined potential surface for the X~3B1 electronic state of methylene CH2
The Journal of Chemical Physics, 79 (3) :1224-1228
198397.
Winter, R.; 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 TeSe
Chemical Physics Letters, 94 (3) :335-338
198396.
Winter, R.; 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 TeSe
Chemical Physics Letters, 94 (3) :335-338
198395.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\) emission of Pl
Chemical Physics Letters, 102 (5) :404-408
198394.
Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b\(^{1}\)\(\Sigma\)\(^{+}\) Emissions from group V-VII diatomic molecules: b0\(^{+}\) → X\(_{1}\)0\(^{+}\) emission of Pl
Chemical Physics Letters, 102 (5) :404-408
198393.
Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeSe
Chemical Physics Letters, 94 (3) :335-338
1983
