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

1986

206.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H\(_{2}\)NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

205.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H\(_{2}\)O and C\(_{3}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

DOI: 10.1016/0022-2852(86)90222-5

204.

Bielefeld, M.; Wildt, J{ü}rgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0\(^{+}\)) + O\(_{2}\)(X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) ↔ SeS(X\(_{1}\)0\(^{+}\)) + O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 126 (5) :421-426
1986

DOI: 10.1016/S0009-2614(86)80128-2

203.

Jensen, Per; Spirko, Vladim{í}r; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Extension to H\(_{2}\)D\(^{+}\) and D\(_{2}\)H\(^{+}\)
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

202.

Jensen, Per; Johns, John W. C.
The infrared spectrum of carbon suboxide in the \(\nu\)\(_{6}\) fundamental region: Experimental observation and semirigid bender analysis
Journal of Molecular Spectroscopy, 118 (1) :248-266
1986

DOI: 10.1016/0022-2852(86)90239-0

201.

Vojt{í}k, Jan; Spirko, Vladim{í}r; Jensen, Per
Vibrational energies of H\(_{3}\)\(^{+}\) and Li\(_{3}\)\(^{+}\) based on the diatomics-in-molecules potentials
Collection of Czechoslovak Chemical Communications, 51 (10) :2057-2062
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19862057

200.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

199.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Vervloet, M.
An electric quadrupole transition: the emission system of oxygen
Canadian Journal of Physics, 64 (3) :242-245
1986
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p86-044

198.

Jensen, Per; Spirko, Vladim{í}r
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

197.

Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.; Beardsworth, R.
The potential surface of X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) and the singlet-triplet splitting
The Journal of Chemical Physics, 85 (7) :3724-3731
1986

DOI: 10.1063/1.450944

196.

Kraemer, Wolfgang P.; Roos, B. O.; Bunker, Philip R.; Jensen, Per
An ab initio calculation of the rotation-vibration energies of the state of CCH using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 120 (1) :236-238
1986

DOI: 10.1016/0022-2852(86)90085-8

195.

Jensen, Per; Bunker, Philip R.
The nonrigid bender Hamiltonian using an alternative perturbation technique
Journal of Molecular Spectroscopy, 118 (1) :18-39
1986

DOI: 10.1016/0022-2852(86)90220-1

194.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.
The high-resolution emission spectrum of S\(_{2}\) in the near infrared: The b\(^{1}\)\(\Sigma\)\(_{g}\)\(^{+}\) - X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\) system
Journal of Molecular Spectroscopy, 119 (2) :377-387
1986

DOI: 10.1016/0022-2852(86)90032-9

193.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H\(_{2}\)NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

192.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H\(_{2}\)O and C\(_{3}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

DOI: 10.1016/0022-2852(86)90222-5

191.

Bielefeld, M.; Wildt, J{ü}rgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0\(^{+}\)) + O\(_{2}\)(X\(^{3}\)\(\Sigma\)\(_{g}\)\(^{-}\)) ↔ SeS(X\(_{1}\)0\(^{+}\)) + O\(_{2}\)(a\(^{1}\)\(\Delta\)\(_{g}\))
Chemical Physics Letters, 126 (5) :421-426
1986

DOI: 10.1016/S0009-2614(86)80128-2

190.

Jensen, Per; Spirko, Vladim{í}r; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H\(_{3}\)\(^{+}\): Extension to H\(_{2}\)D\(^{+}\) and D\(_{2}\)H\(^{+}\)
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

DOI: 10.1016/0022-2852(86)90047-0

189.

Jensen, Per; Johns, John W. C.
The infrared spectrum of carbon suboxide in the \(\nu\)\(_{6}\) fundamental region: Experimental observation and semirigid bender analysis
Journal of Molecular Spectroscopy, 118 (1) :248-266
1986

DOI: 10.1016/0022-2852(86)90239-0

188.

Vojt{í}k, Jan; Spirko, Vladim{í}r; Jensen, Per
Vibrational energies of H\(_{3}\)\(^{+}\) and Li\(_{3}\)\(^{+}\) based on the diatomics-in-molecules potentials
Collection of Czechoslovak Chemical Communications, 51 (10) :2057-2062
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19862057

187.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC\(^{+}\) calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

186.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Ab initio rotation-vibration energies of HOC+ calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :40-49
1986

DOI: 10.1016/0022-2852(86)90221-3

185.

Fink, Ewald H.; Kruse, H.; Ramsay, D. A.; Vervloet, M.
An electric quadrupole transition: the emission system of oxygen
Canadian Journal of Physics, 64 (3) :242-245
1986
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/p86-044

184.

Jensen, Per; Winnewisser, Manfred
Prediction of higher inversion energy levels for isocyanamide H2NNC
Collection of Czechoslovak Chemical Communications, 51 (7) :1373-1381
1986
Herausgeber: Institute of Organic Chemistry and Biochemistry AS CR, v.v.i.

DOI: 10.1135/cccc19861373

183.

Jensen, Per; Spirko, Vladimír
A new Morse-oscillator based Hamiltonian for H3+: Calculation of line strengths
Journal of Molecular Spectroscopy, 118 (1) :208-231
1986

DOI: 10.1016/0022-2852(86)90236-5

182.

Tausch, Michael W.
Silberfreie Photographie und Photochromie
Praxis der Naturwissenschaften (Chemie), 35 :19
1986