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
- 2025
5385.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5384.
Sinani, Mario; Wynn, Andrew; Palacios, Rafael
Physics-Informed Data-Driven Modelling of Nonlinear Aerodynamic Forces of the Pazy Wing
AIAA SciTech Forum, 6-10 January
01 20255383.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Schrader, Claudia
Produktion eigener VR-Lernsettings im Projekt FoPro-VR. Ein interdisziplinärer Lehransatz für die Lehramtsausbildung
In Mrohs, Lorenz; Franz, Julia; Herrmann, Dominik; Lindner, Konstantin; Staake, Thorsten, Editor, Digitales Lehren und Lernen an der Hochschule. Strategien - Bedingungen - Umsetzung
Seite 191-204
Herausgeber: transcript, Bielefeld
2025
191-204ISBN: 9783839471203
5382.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
PNAS
20255381.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
20255380.
Liu, Qian; Yanchang, Zhang; Zuan, Wang; Wang, Miao; Zhao, Xiaowei
Small-signal stability of sequence-decomposed grid-forming IBRs with DC-link voltage dynamics
Februar 20255379.
Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
20255378.
Santos, Daniela Dos; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the Multiobejctive Quasi-Clique Problem
European Journal of Operational Research, 323 :409—424
20255377.
Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation
Januar 20255376.
Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society5375.
Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings5374.
Günther, Michael
Einführung in die Finanzmathematik5373.
Al{\i}, G; Bartel, A
Electrical RLC networks and diodes5372.
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 :5875371.
Ehrhardt, Matthias
für Angewandte Analysis und Stochastik5370.
Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations5369.
High order tensor product interpolation in the Combination Technique
preprint, 14 :255368.
Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 3885367.
Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers5366.
Günther, Michael
Lab Exercises for Numerical Analysis and Simulation I: ODEs5365.
Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics5364.
Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics5363.
Ehrhardt, Matthias; Günther, Michael
Mathematical Study of Grossman's model of investment in health capital5362.
Bartel, PD Dr A
Mathematische Modellierung in Anwendungen5361.
Model Order Reduction Techniques for Basket Option Pricing