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
- 2021
4566.
Günther, Michael; Bartel, Andreas; Jacob, Birgit; Reis, Timo
Dynamic iteration schemes and port-Hamiltonian formulation in coupled differential-algebraic equation circuit simulation
International Journal of Circuit Theory and Applications, 49 (2) :430–452
2021
Herausgeber: John Wiley & Sons4565.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
E-Book-flankiertes Experimentalkonzept zu mikrobiellen Brennstoffzellen in der Sekundarstufe II
Digitalisation in Chemistry Education. Digitales Lehren und Lernen an Hochschule und Schule im Fach Chemie
Seite 133-141
Herausgeber: Johannes Huwer, Amitabh Banerji und Nicole Graulich, Waxmann, Münster
2021
133-141ISBN: 978-3-8309-4418-8
4564.
Felpel, M.; Kienitz, J.; McWalter, T. A.
Effective stochastic volatility: Applications to {ZABR}-type models
Quantitative Finance, 21 (5) :837-852
2021
Herausgeber: Routledge4563.
Felpel, M.; Kienitz, J.; McWalter, T. A.
Effective stochastic volatility: applications to ZABR-type models
Quantitative Finance, 21 (5) :837–852
2021
Herausgeber: Routledge4562.
Haussmann, N.; Zang, M.; Stroka, S.; Mease, R.; Schmuelling, B.; Clemens, M.
Efficient Assessment of the Human Exposure to Low-Frequency Magnetic Fields Based on Free Space Field Measurements
23rd International Conference on the Computation of Electromagnetic Fields (COMPUMAG 2021), Cancun, Mexico, Online Conference, 16.-21.01.2022. Two-page digest submitted.
20214561.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Eigenstructure and iterates for uniquely ergodic Kantorovich modifications of operators II
Positivity, 25 :1585-1599
20214560.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Eine Lehrkräfte-Fortbildung im Portrait: Lowcost Experimente zu verschiedenen Brennstoffzelltypen für den Einsatz im Chemieunterricht.
CHEMKON
20214559.
Alameddine, Jean-Marco; others
Electromagnetic Shower Simulation for CORSIKA 8
PoS, ICRC2021 :428
20214558.
Viviani, Emma; Di Persio, Luca; Ehrhardt, Matthias
Energy markets forecasting. From inferential statistics to machine learning: The German case
Energies, 14 (2) :364
2021
Herausgeber: MDPI4557.
Viviani, Emma; Di Persio, Luca; Ehrhardt, Matthias
Energy markets forecasting. From inferential statistics to machine learning: The German case
Energies, 14 (2) :364
2021
Herausgeber: MDPI4556.
Viviani, Emma; Di Persio, Luca; Ehrhardt, Matthias
Energy Markets Forecasting. From Inferential Statistics to Machine Learning: The German Case
Energies, 14 (2) :364
Januar 2021
Herausgeber: MDPI
ISSN: 1996-10734555.
Energy Markets Forecasting. From Inferential Statistics to Machine Learning: The German Case. Energies 2021, 14, 364
20214554.
Kossaczk{\'a}, Tatiana; Ehrhardt, Matthias; Günther, Michael
Enhanced fifth order {WENO} shock-capturing schemes with deep learning
Res. Appl. Math., 12 :100201
2021
Herausgeber: Elsevier4553.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Enhanced fifth order WENO shock-capturing schemes with deep learning
Results in Applied Mathematics, 12 :100201
2021
Herausgeber: Elsevier4552.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Enhanced fifth order WENO shock-capturing schemes with deep learning
Results in Applied Mathematics, 12 :100201
2021
Herausgeber: Elsevier4551.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Enhanced fifth order WENO shock-capturing schemes with deep learning
Results in Applied Mathematics, 12 :100201
2021
Herausgeber: Elsevier4550.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Enhanced fifth order WENO shock-capturing schemes with deep learning
Results in Applied Mathematics, 12 :100201
2021
Herausgeber: Elsevier4549.
Farkas, Bálint; Csomós, Petra; Kovács, Balázs
Error estimates for a splitting integrator for semilinear boundary coupled systems
IMA J. Numerical Analysis
20214548.
Stapmanns, J.; Hahne, J.; Helias, M.; Bolten, Matthias; Diesmann, M.; Dahmen, D.
Event-based update of synapses in voltage-based learning rules
Front. Neuroinform., 15 :15
20214547.
Stapmanns, J.; Hahne, J.; Helias, M.; Bolten, M.; Diesmann, M.; Dahmen, D.
Event-based update of synapses in voltage-based learning rules
Front. Neuroinform., 15 :15
20214546.
Stapmanns, J.; Hahne, J.; Helias, M.; Bolten, M.; Diesmann, M.; Dahmen, D.
Event-based update of synapses in voltage-based learning rules
Front. Neuroinform., 15 :15
20214545.
Glück, Jochen; Mugnolo, Delio
Eventual domination for linear evolution equations
Math. Z., 299 (3-4) :1421--1443
20214544.
Abreu, Pedro; others
Expected performance of the AugerPrime Radio Detector
PoS, ICRC2021 :262
20214543.
Tovar, Carmen M.; Haack, Alexander; Barnes, Ian; Bejan, Iustinian Gabriel; Wiesen, Peter
Experimental and theoretical study of the reactivity of a series of epoxides with chlorine atoms at 298 K
Physical Chemistry Chemical Physics, 23 (9) :5176-5186
20214542.
Tovar, Carmen M.; Haack, Alexander; Barnes, Ian; Bejan, Iustinian Gabriel; Wiesen, Peter
Experimental and theoretical study of the reactivity of a series of epoxides with chlorine atoms at 298 K
Physical Chemistry Chemical Physics, 23 (9) :5176-5186
2021