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
- 2022
4866.
Sch\"afers, Torben; Teng, Long
Asymmetry in stochastic volatility models with threshold and time-dependent correlation
Studies in Nonlinear Dynamics \& Econometrics
20224865.
Xue, Chaoyang; Ye, Can; Kleffmann, Jörg; Zhang, Chenglong; Catoire, Valéry; Bao, Fengxia; Mellouki, Abdelwahid; Xue, Likun; Chen, Jianmin; Lu, Keding; Zhao, Yong; Liu, Hengde; Guo, Zhaoxin; Mu, Yujing
Atmospheric measurements at Mt. Tai – Part I: HONO formation and its role in the oxidizing capacity of the upper boundary layer
Atmospheric Chemistry and Physics, 22 (5) :3149—3167
März 2022
ISSN: 1680-73244864.
Rottmann, Matthias; Reese, Marco
Automated Detection of Label Errors in Semantic Segmentation Datasets via Deep Learning and Uncertainty Quantification
20224863.
Forget, Nicolas; Gadegaard, Sune Lauth; Klamroth, Kathrin; Nielsen, Lars Relund; Przybylski, Anthony
Branch-and-bound and objective branching with three or more objectives
Computers & Operations Research, 148
2022
ISSN: 0305-05484862.
Paquete, Luís; Schulze, Britta; Stiglmayr, Michael; Lourenço, Ana Catarina
Computing Representations using Hypervolume Scalarizations
Computers and Operations Research, 137 :105349
20224861.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Correlation matrices driven by stochastic isospectral flows
Progress in Industrial Mathematics at ECMI 2021, Seite 455–461
Herausgeber: Springer Cham
20224860.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Correlation matrices driven by stochastic isospectral flows
Progress in Industrial Mathematics at ECMI 2021, Seite 455–461
Herausgeber: Springer Cham
20224859.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Correlation matrices driven by stochastic isospectral flows
Progress in Industrial Mathematics at ECMI 2021, Seite 455–461
Herausgeber: Springer Cham
20224858.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael
Correlation Matrices Driven by Stochastic Isospectral Flows
Progress in Industrial Mathematics at ECMI 2021
Seite 455--461
Herausgeber: Springer International Publishing Cham
2022
455--4614857.
Arora, Sahiba; Glück, Jochen
Criteria for eventual domination of operator semigroups and resolvents
To appear in the Proceedings of IWOTA 2021, Lancaster
20224856.
Anna Braun, geboren Tscherniewski
Crowd Management at Train Stations in Case of Large-Scale Emergency Events
Bergische Universität Wuppertal
20224855.
Alves Batista, Rafael; others
CRPropa 3.2 -- an advanced framework for high-energy particle propagation in extragalactic and galactic spaces
JCAP, 09 :035
20224854.
Schweitzer, Marcel
Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian
Electron. Trans. Numer. Anal., 55 :438-454
20224853.
Schweitzer, Marcel
Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian
Electron. Trans. Numer. Anal., 55 :438-454
20224852.
Schweitzer, Marcel
Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian
Electron. Trans. Numer. Anal., 55 :438-454
20224851.
Stiglmayr, Michael; Figueira, Jos\'{e} Rui; Klamroth, Kathrin; Paquete, Lu\'{i}s; Schulze, Britta
Decision Space Robustness for Multiobjective Integer Linear Programming
Annals of Operations Research, 319 :1769--1791
20224850.
Stiglmayr, Michael; Uhlemeyer, Svenja; Uhlemeyer, Björn; Zdrallek, Markus
Determining Cost-Efficient Controls of Electrical Energy Storages Using Dynamic Programming
20224849.
Development of a gas chromatography-mass spectrometry (GC-MS) method for the analysis of triterpenic acids
Lebensmittelchemie, 76 :S2-338-S2-338
2022
Herausgeber: Wiley
ISSN: 0937-14784848.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Digitalisierung: Mit einem E‐Book in die organische Chemie starten
Nachrichten aus der Chemie, 70 (1) :34-36
20224847.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
Discrete port-Hamiltonian coupled heat transfer
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021, Seite 439–445
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224846.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
Discrete port-Hamiltonian coupled heat transfer
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021, Seite 439–445
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224845.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
Discrete port-Hamiltonian coupled heat transfer
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021, Seite 439–445
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224844.
Jäschke, Jens; Ehrhardt, M.; Günther, M.; Jacob, Birgit
Discrete port-Hamiltonian Coupled Heat Transfer
Progress in Industrial Mathematics at ECMI 2021, The European Consortium for Mathematics in Industry, Seite 439-445
In M. Ehrhardt and M. Günther, Editor
Herausgeber: Springer
20224843.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
Discrete port-Hamiltonian coupled heat transfer
Progress in Industrial Mathematics at ECMI 2021
Seite 439--445
Herausgeber: Springer International Publishing Cham
2022
439--4454842.
Edeko, Nikolai; Kreidler, Henrik
Distal systems in topological dynamics and ergodic theory
2022