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

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

214.

Weinmüller, E.; Winkler, E.
Path-following Algorithm for Singular Boundary Value Problems
ZAMM, 68 :527--537
1988

213.

Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(\(^{3}\)P) atoms in halogenomethane + H flame systems and measurements of C(\(^{3}\)P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988

DOI: 10.1039/f29888400455

212.

Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(\(^{3}\)P) atoms in halogenomethane + H flame systems and measurements of C(\(^{3}\)P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988

DOI: 10.1039/f29888400455

211.

Becker, Karl Heinz; Brockmann, Klaus Josef; Wiesen, Peter
Spectroscopic identification of C(3P) atoms in halogenomethane + H flame systems and measurements of C(3P) reaction rate constants by two-photon laser-induced fluorescence
Journal of the Chemical Society, Faraday Transactions 2, 84 (5) :455-461
1988

DOI: 10.1039/f29888400455

210.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

DOI: 10.1016/0022-2852(88)90112-9

209.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

DOI: 10.1016/0022-2852(88)90112-9

208.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a1Δ(a2)-X3Σ-(X21) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

DOI: 10.1016/0022-2852(88)90112-9

207.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

206.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

205.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X~3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

DOI: 10.1063/1.455184

1987

204.

Spirko, Vladim{í}r; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

203.

Spirko, Vladim{í}r; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

202.

Spirko, Vladimír; Cejchan, A.; Jensen, Per
A new Morse-oscillator based Hamiltonian for H3+: Explicit expressions for some vibrational matrix elements
Journal of Molecular Spectroscopy, 124 (2) :430-436
1987

DOI: 10.1016/0022-2852(87)90152-4

201.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of \(\nu\)\(_{1}\) and \(\nu\)\(_{3}\) for triplet methylene (X\verb=~=\(^{3}\)B\(_{1}\) CH\(_{2}\)) and the determination of the vibrationless singlet-triplet splitting Te (a\verb=~=\(^{1}\)A\(_{1}\))
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

200.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of \(\nu\)\(_{1}\) and \(\nu\)\(_{3}\) for triplet methylene (X\verb=~=\(^{3}\)B\(_{1}\) CH\(_{2}\)) and the determination of the vibrationless singlet-triplet splitting Te (a\verb=~=\(^{1}\)A\(_{1}\))
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

199.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH\(_{2}\)\(^{+}\) using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

198.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH\(_{2}\)\(^{+}\) using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

197.

Jensen, Per; Bunker, Philip R.; McLean, A. D.
An ab initio calculation of the rotation-vibration energies of singlet and triplet NH2+ using the morbid Hamiltonian
Chemical Physics Letters, 141 (1-2) :53-57
1987

DOI: 10.1016/0009-2614(87)80091-X

196.

McLean, A. D.; Bunker, Philip R.; Escribano, R. M.; Jensen, Per
An ab initio calculation of ν1 and ν3 for triplet methylene (X~3B1 CH2) and the determination of the vibrationless singlet-triplet splitting Te (a~1A1)
The Journal of Chemical Physics, 87 (4) :2166-2169
1987

DOI: 10.1063/1.453141

195.

Heilmann, Margareta
Approximation auf [0, ∞) durch das Verfahren der Operatoren vom Baskakov-Durrmeyer Typ
Universität Dortmund
1987

194.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987

DOI: 10.1016/0022-2852(87)90061-0

193.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
Calculated rotation-vibration energies for HOC\(^{+}\)
Journal of Molecular Spectroscopy, 121 (2) :450-452
1987

DOI: 10.1016/0022-2852(87)90061-0