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

5542.


Oxidative Cleavage of β-Substituted Primary Alcohols in Flow
Organic Letters
01 2026
Herausgeber: ACS
ISSN: 1523-7052

5541.

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

5540.

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

5539.

Günther, Michael
Einführung in die Finanzmathematik

5538.

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

5537.

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

5536.

Ehrhardt, Matthias
für Angewandte Analysis und Stochastik

5535.

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

5534.


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

5533.

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

5532.

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

5531.

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

5530.

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

5529.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5528.

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

5527.

Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

5526.


Model Order Reduction Techniques for Basket Option Pricing

5525.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

5524.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

5523.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

5522.

Putek, Piotr; PAPLICKI, Piotr; Pulch, Roland; Maten, Jan; Günther, Michael; PA{\L}KA, Ryszard
NONLINEAR MULTIOBJECTIVE TOPOLOGY OPTIMIZATION AND MULTIPHYSICS ANALYSIS OF A PERMANENT-MAGNET EXCITED SYNCHRONOUS MACHINE

5521.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

5520.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

5519.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

5518.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit
Operator Splitting and Multirate Schemes