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

178.

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

177.

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

176.

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

175.

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

174.

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

173.

Jensen, Per; Spirko, Vladimír; Bunker, Philip R.
A new Morse-oscillator based Hamiltonian for H3+: Extension to H2D+ and D2H+
Journal of Molecular Spectroscopy, 115 (2) :269-293
1986

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

172.

Adams, Warren P; Sherali, Hanif D
A tight linearization and an algorithm for zero-one quadratic programming problems
Management Science, 32 (10) :1274--1290
1986
Herausgeber: INFORMS

171.

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

170.

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

169.

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

168.

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

167.

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

166.

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

165.

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

164.

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

163.

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

162.

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

161.

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

160.

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

159.

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

158.

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

157.

Bielefeld, M.; Wildt, Jürgen; Fink, Ewald H.
Rate constants of the near-resonant E-E energy exchange processes SeS(b0+) + O2(X3Σg-) ↔ SeS(X10+) + O2(a1Δg)
Chemical Physics Letters, 126 (5) :421-426
1986

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

156.

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

155.

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

154.

Beardsworth, R.; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
Rotation-vibration energy levels of H2O and C3 calculated using the nonrigid bender Hamiltonian
Journal of Molecular Spectroscopy, 118 (1) :50-63
1986

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