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



2026

5587.

Vinod, Vivin; Zaspel, Peter
Improvise, Adapt, Overcome: An On-The-Fly Multifidelity Algorithm for Efficient Machine Learning
2026

5586.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Kernels for composition of positive linear operators
Journal of Mathematical Analysis and Applications, 555 (2) :130052
2026
ISSN: 0022-247X

5585.

Zeller, Diana; Bohrmann-Linde, Claudia
KI-Chatbots als Unterrichtswerkzeug: Eine Lehrkräftefortbildung zum Einsatz von KI-Chatbots im Chemieunterricht
CHEMKON, 33/3 :71-76
2026

5584.

Abel, Ulrich; Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,ınfty)$
2026

5583.

Abel, Ulrich; Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,ınfty)$
2026

5582.

Vinod, Vivin; Zaspel, Peter
LFaB: Low Fidelity as Bias for Active Learning in the Chemical Configuration Space
J. Chem. Theory Comput., 22 (11) :5637-5648
2026

5581.

Könen, David; Stiglmayr, Michael
Output-sensitive Complexity of Multi-Objective Integer Network Flow Problems
Journal of Combinatorial Optimization, 51 (14)
2026

5580.

Yuden, Kezang; Nemesch, Levin; Ruzika, Stefan
Parametric Biobjective Linear Programming
2026

5579.

Abel, Ulrich; Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Positive linear operators fixing two prescribed functions
2026

5578.

Lopes, Gonçalo; Klamroth, Kathrin; Paquete, Luís
Solving hypervolume scalarizations for MOCO problems
2026

5577.

Schaub, Louise; Zaspel, Peter
Variational Free Energy Pivot Selection for Pivoted Cholesky
arXiv preprint
2026

5576.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society

5575.

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

5574.

Günther, Michael
Einführung in die Finanzmathematik

5573.

Al{\i}, G; Bartel, A
Electrical RLC networks and diodes

5572.

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

5571.

Ehrhardt, Matthias
für Angewandte Analysis und Stochastik

5570.

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

5569.


High order tensor product interpolation in the Combination Technique
preprint, 14 :25

5568.

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

5567.

Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers

5566.

Günther, Michael
Lab Exercises for Numerical Analysis and Simulation I: ODEs

5565.

Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics

5564.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5563.

Ehrhardt, Matthias; Günther, Michael
Mathematical Study of Grossman's model of investment in health capital