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
- 1998
762.
Shestakov, Oleg; Gielen, R.; Pravilov, A. M.; Setzer, Klaus-Dieter; Fink, Ewald H.
LIF study of the b1Σ+(b0+) ↔ X3Σ-(X10+,X21) transitions of SbH and SbD
Journal of Molecular Spectroscopy, 191 (1) :199-205
1998
Herausgeber: Academic Press761.
Bartel, A.
MultiROW within P-Star. A Feasibility Study
Unclassified NatLab Report No. 1998/824
Herausgeber: Philips Electronics
1998760.
Gilg, A
Numerical circuit simulation Grund, F, s Borchardt, J Gunther, M, s Gilg, A
Surveys on Mathematics for Industry, 8 (3) :165--170
1998
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.759.
Le Tallec, P; Perlat, JP; Struckmeier, J
Numerical modeling of gas flows in the transition between rarefied and continuum regimes
Numerical Flow Simulation I: CNRS-DFG Collaborative Research Programme, Results 1996--1998 :222--241
1998
Herausgeber: Springer Berlin Heidelberg758.
Wöhrle, D.; Tausch, Michael W.; Stohrer, W.-D.
PHOTOCHEMIE - Konzepte, Methoden, Experimente
Herausgeber: Wiley-VCH, Weinheim
1998757.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237<λ<270) nm and at 205 nm and the velocity distribution of O(1D) atoms
Chemical Physics Letters, 282 (3-4) :292-298
1998756.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237
Chemical Physics Letters, 282 (3-4) :292-298
1998755.
Schmidt, Sven; Benter, Thorsten; Schindler, Ralph N.
Photodissociation dynamcis of ClO radicals in the range (237
Chemical Physics Letters, 282 (3-4) :292-298
1998754.
Günther, Michael
Simulating digital circuits numerically - a charge-oriented ROW approach
Numerische Mathematik, 79 (2) :203–212
1998
Herausgeber: Springer New York753.
G\"unther, Michael
Simulating digital circuits numerically -- a charge-oriented {ROW} approach
Numer.~Math., 79 :203--212
1998752.
Günther, Michael
Simulating digital circuits numerically--a charge-oriented ROW approach
Numerische Mathematik, 79 (2) :203--212
1998
Herausgeber: Springer-Verlag751.
Tausch, Michael W.
Sinn(e) der Fachdidaktik
{CHEMKON}, 5 (4) :173--173
1998
Herausgeber: Wiley750.
Becker, Karl Heinz; Kleffmann, J{ö}rg; Negri, R. Martin; Wiesen, Peter
Solubility of nitrous acid (HONO) in ammonium sulfate solutions
Journal of the Chemical Society - Faraday Transactions, 94 (11) :1583-1586
1998
Herausgeber: The Royal Society of Chemistry749.
Becker, Karl Heinz; Kleffmann, J{ö}rg; Negri, R. Martin; Wiesen, Peter
Solubility of nitrous acid (HONO) in ammonium sulfate solutions
Journal of the Chemical Society - Faraday Transactions, 94 (11) :1583-1586
1998
Herausgeber: The Royal Society of Chemistry748.
Becker, Karl Heinz; Kleffmann, Jörg; Negri, R. Martin; Wiesen, Peter
Solubility of nitrous acid (HONO) in ammonium sulfate solutions
Journal of the Chemical Society - Faraday Transactions, 94 (11) :1583-1586
1998
Herausgeber: The Royal Society of Chemistry747.
[german] Tausch, Michael W.; Grolmuss, A.; Woock, M.
Vom Lichtquant zum Sehreiz
Praxis der Naturwissenschaften (Physik), 47 (5) :26
1998- 1997
746.
Arnold, A.; Ehrhardt, M.
A New Discrete Transparent Boundary Condition for Standard and Wide Angle 'Parabolic' Equations in Underwater Acoustics
Proceedings of the Third International Conference on Theoretical and Computational Acoustics, July 14-18, 1997, Newark, New Jersey, USA, Seite 623-635
1997745.
Ehrgott, Matthias; Hamacher, Horst W.; Klamroth, Kathrin; Nickel, Stefan; Schöbel, Anita; Wiecek, Margaret M.
A note on the equivalence of balance points and Pareto solutions in multiple objective programming
Journal of Optimization Theory and Applications, 92 :209-212
1997744.
G{{\'o}}mez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H\(_{2}\)Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press743.
G{{\'o}}mez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H\(_{2}\)Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press742.
Gómez, P. C.; Jensen, Per
A potential energy surface for the electronic ground state of H2Te derived from experiment
Journal of Molecular Spectroscopy, 185 (2) :282-289
1997
Herausgeber: Academic Press741.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH\(_{2}\)\(^{+}\)
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland740.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH\(_{2}\)\(^{+}\)
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland739.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
A theoretical calculation of the absorption spectrum of CH2+
Chemical Physics, 225 (1-3) :33-54
1997
Herausgeber: North-Holland738.
Kozin, Igor N.; Jensen, Per; Li, Yan; Buenker, Robert J.; Hirsch, Gerhard; Klee, Stefan
An ab initio calculation of the dipole moment surfaces and the vibrational transition moments of the H\(_{2}\)Te molecule
Journal of Molecular Spectroscopy, 181 (1) :108-118
1997
Herausgeber: Academic Press
