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

5553.

Tapera, Michael; Savvidis, Athanasios; Meysing, Cedric; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidative Cleavage of β-Substituted Primary Alcohols in Flow
Organic Letters
Januar 2026
Herausgeber: ACS
ISSN: 1523-7052

5552.

Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Boundary control systems on a one-dimension spatial domain
2026

5551.

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

5550.

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

5549.

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

5548.

Günther, Michael
Einführung in die Finanzmathematik

5547.

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

5546.

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

5545.

Ehrhardt, Matthias
für Angewandte Analysis und Stochastik

5544.

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

5543.


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

5542.

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

5541.

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

5540.

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

5539.

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

5538.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5537.

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

5536.

Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

5535.


Model Order Reduction Techniques for Basket Option Pricing

5534.

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

5533.

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

5532.

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

5531.

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

5530.

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

5529.

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