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



2024

6855.

Bauß, Julius; Stiglmayr, Michael
Adapting Branching and Queuing for Multi-objective Branch and Bound
Operations Research Proceedings 2023
Herausgeber: Springer
2024
2023

6854.

[german] Kiesling, Elisabeth; Kremer, Richard; Pereira Vaz, Nuno; Venzlaff, Julian; Bohrmann-Linde, Claudia
Wege aus der Klimakrise – ein BNE-Schülerlaborangebot mit mehrdimensionalem Zugang
MNU Journal, 76 (06/2023)
November 2023
ISSN: 0025-5866

6853.

[english] Venzlaff, Julian; Kosumi, Kaltrina; Zeller, Diana; Bohrmann-Linde, Claudia
Education for Sustainable Development and Experiments involving Titanium Dioxide
World Journal of Chemical Education, 11 (3) :80-86
August 2023

6852.

[english] Brunnert, Rainer; Tausch, Michael W.
Green Chemistry in STEM Education: Light for Basic Concepts
World Journal of Chemical Education, 11 (3) :65-73
August 2023

6851.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit
August 2023

6850.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A numerical study of the impact of variance boundary conditions for the Heston model
IMACM preprint 23/11
Juli 2023

6849.

[german] Venzlaff, Julian; Bohrmann-Linde, Claudia
Photoreformierung – grüner Wasserstoff aus Alkohol, Zucker und Stärke
CHEMKON, 30 (6) :254-259
Juni 2023

6848.

Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry
05 2023

6847.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Dem Apfel ans Leder
Nachrichten aus der Chemie, 71 :12-14
März 2023

6846.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6845.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6844.

Günther, Michael
Einführung in die Finanzmathematik

6843.

Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :587

6842.

Ehrhardt, Matthias; Zheng, Chunxiong
für Angewandte Analysis und Stochastik

6841.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6840.

Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations

6839.

Tripiccione, Betreuer Raffaele; Ehrhardt, Matthias; Alexandrou, Constantia; Toschi, Federico; Simma, Hubert; Schifano, Co-Betreuer Sebastiano Fabio
Daniele Simeoni 1836010

6838.

Hendricks, C; Ehrhardt, M; Günther, M
High order tensor product interpolation in the Combination Technique
preprint, 14 :25

6837.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

6836.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

6835.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers

6834.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csomós, Petra; Faragó, István; Fekete, Imre; others
Invited Papers

6833.

Günther, Michael; Kossaczk{\`y}, Igor
Lab Exercises for Numerical Analysis and Simulation I: ODEs

6832.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6831.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

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