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

1987: 182.
Tausch, Michael W.; Fischer, W.; Glöckner, W.; Köhler-Degner, M.; Nöding, S.; Wolf, H.
STOFF UND FORMEL - Chemiebuch für Gymnasien; Ausgabe NRW, S I, 291 Seiten
Herausgeber: C. C. Buchner, Bamberg
1987; 181.
Tausch, Michael W.; Fischer, W.; Glöckner, W.; Köhler-Degner, M.; Nöding, S.; Wolf, H.
STOFF UND FORMEL - Lehrerbände mit didaktischen Hinweisen und Lösungen der Aufgaben zu STOFF UND FORMEL - Chemiebuch für Gymnasien und Ausgabe NRW
Herausgeber: C. C. Buchner, Bamberg
1987
1986: 180.
Maten, E. Jan W.; Sleijpen, Gerard L. G.
A convergence analysis of Hopscotch methods for fourth order parabolic equations
Numerische Mathematik, 49 (2-3) :275--290
März 1986
Herausgeber: Springer Science and Business Media {LLC}
DOI: 10.1007/bf01389630; 179.
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; 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; 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; 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, 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; 174.
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; 173.
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; 172.
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; 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.
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; 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.
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; 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.
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; 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 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; 160.
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; 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, 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

Index Analysis

Group members working on that field

Cooperations

Publications

182.

181.

180.

179.

178.

177.

176.

175.

174.

173.

172.

171.

170.

169.

168.

167.

166.

165.

164.

163.

162.

161.

160.

159.

158.