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

2004

1279.

Appel, Matthew F.; McKeachie, J. Ryan; van der Veer, Wytze E.; Benter, Thorsten
Simple induction probe electric field meter for the detection of electrical fields generated by ion-optical electrodes
Review of Scientific Instruments, 75 (8) :2603-2607
2004

DOI: 10.1063/1.1765751

1278.

Ehrhardt, M.; Mickens, R. E.
Solutions to the Discrete {Airy} Equation: Application to Parabolic Equation Calculations
JCAM, 172 (1) :183--206
2004

1277.

Ehrhardt, Matthias
Solutions to the discrete Airy equation: Application to parabolic equation calculations
Journal of Computational and Applied Mathematics, 172 (1) :183–206
2004
Herausgeber: North-Holland

DOI: 10.1016/j.cam.2004.02.011

1276.

Ehrhardt, Matthias
Solutions to the discrete Airy equation: Application to parabolic equation calculations
Journal of computational and applied mathematics, 172 (1) :183--206
2004
Herausgeber: Elsevier

1275.

Winkin, Joseph J.; Callier, Frank M.; Jacob, Birgit; Partington, Jonathan R.
Spectral factorization by symmetric extraction for distributed parameter systems
SIAM J. Control Optim., 43 (4) :1435--1466
2004

DOI: 10.1137/S0363012902416456

1274.

Winkler, R.
Stochastic {DAEs} in Transient Noise Simulation
In Schilders, W. and ter Maten, J. and Houben, S., Editor, Scientific Computing in Electrical Engineering at SCEE 2002, Seite 408--415
In Schilders, W. and ter Maten, J. and Houben, S., Editor
Herausgeber: Springer
2004

1273.

Kahl, Christian; Günther, Michael; Roßberg, Thilo
Structure preserving stochastic integration schemes in interest rate derivative modeling
Applied Numerical Mathematics, 58 (3) :284--295
2004
Herausgeber: North-Holland

1272.

Rommes, J.; Bomhof, C. W.; Vorst, H. A.; Maten, E. J. W.
The Application of Preconditioned {Jacobi-Davidson} Methods in Pole-zero Analysis
In W. H. A. Schilders and E. J. W. ter Maten and S. H. M. J. Houben, Editor, Scientific Computing in Electrical Engineering at SCEE 2002, Eindhoven Band 4 aus Mathematics in Industry
Seite 349--355
Herausgeber: Springer Berlin Heidelberg
2004
349--355

DOI: 10.1007/978-3-642-55872-6_38

1271.

Abel, Ulrich; Heilmann, Margareta
The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights
Mediterranean Journal of Mathematics, 1 (4) :487-499
2004

DOI: 10.1007/s00009-004-0026-2

1270.

Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH\(_{2}\)
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/v04-030

1269.

Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH\(_{2}\)
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/v04-030

1268.

Yurchenko, Sergey N.; Bunker, Philip R.; Kraemer, Wolfgang P.; Jensen, Per
The spectrum of singlet SiH2
Canadian Journal of Chemistry, 82 (6) :694-708
2004
Herausgeber: NRC Research Press Ottawa, Canada

DOI: 10.1139/v04-030

1267.

Bartel, A
Thermal Models in Electric Circuit Design
, Scientific Computing in Electrical Engineering: Proceedings of the SCEE-2002 Conference held in EindhovenBand4, Seite 104
Springer Science & Business Media
2004

1266.

Striebel, M
Towards One-Step Multirate Methods in Chip Design
Preprint IMACM
2004
Herausgeber: Bergische Universität Wuppertal

Download

1265.

Striebel, M
Towards One-Step Multirate Methods in Chip Design
:129--126
2004
Herausgeber: Springer-Verlag, Berlin

1264.

Striebel, M
Towards One-Step Multirate Methods in Chip Design
Preprint IMACM
2004
Herausgeber: Bergische Universität Wuppertal

Download

1263.

Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H\(_{2}\)O\(^{+}\)
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press

DOI: 10.1016/j.jms.2004.02.011

1262.

Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H\(_{2}\)O\(^{+}\)
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press

DOI: 10.1016/j.jms.2004.02.011

1261.

Wu, Shenghai; Chen, Yangqin; Yang, Xiaohua; Guo, Yingchun; Liu, Yuyan; Li, Yan; Buenker, Robert J.; Jensen, Per
Vibronic transition moments and line intensities for H2O+
Journal of Molecular Spectroscopy, 225 (1) :96-106
2004
Herausgeber: Academic Press

DOI: 10.1016/j.jms.2004.02.011

1260.

Bohrmann-Linde, Claudia
Von der Elektrolysezelle zur Leuchtdiode - Elektrolumineszenz im Chemieunterricht
Praxis der Naturwissenschaften - Chemie in der Schule, 56 (6)
2004

1259.

Jacob, Birgit
What is the better signal space for discrete-time systems: l_2(\Bbb Z) or l_2(\Bbb N_0)?
SIAM J. Control Optim., 43 (4) :1521--1534
2004

DOI: 10.1137/S0363012902412471

1258.

Tausch, Michael W.
Zink - Ein Element von A bis Z
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (7) :1
2004

1257.

Tausch, Michael W.; Rohe, Bernd
Zinksulfat - Ein technisches Produkt mit didaktisch interessanten Facetten
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (7) :21
2004
2003

1256.

Houben, S. H. M. J.; Maten, E. J. W.; Sevat, M.F.
A new transient integration method for free-running oscillators
In R. Vahrmann, Editor, Analog 2003 -- Entwicklung von Analogschaltungen mit CAE-Methoden mit dem Schwerpunkt Entwurfsverfahren für Automotive-Anwendungen, Seite 61-66
In R. Vahrmann, Editor
September 2003

1255.

Feldmann, Jorg-Uwe; Günther, Michael
Simulation apparatus and simulation method for a system having analog and digital elements
August 2003