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
- 2020
4341.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
SN Partial Differential Equations and Applications, 1 (2) :1–34
2020
Herausgeber: Springer International Publishing4340.
Aab, Alexander; others
A Search for Ultra-high-energy Neutrinos from TXS 0506+056 Using the Pierre Auger Observatory
Astrophys. J., 902 (2) :105
20204339.
Kühn, J.; Bartel, A.; Putek, P.
A Thermal Extension of Tellinen's Scalar Hysteresis Model
, Scientific Computing in Electrical Engineering SCEE 2018BandXausMathematics in Industry
Herausgeber: Springer, Berlin
20204338.
Kühn, Jan; Bartel, Andreas; Putek, Piotr
A thermal extension of Tellinen’s scalar hysteresis model
In Nicosia, Giuseppe and Romano, Vittorio, Editor, Scientific Computing in Electrical Engineering: SCEE 2018, Taormina, Italy, September 2018ausMathematics in Industry, Seite 55–63
In Nicosia, Giuseppe and Romano, Vittorio, Editor
Herausgeber: Springer Cham
20204337.
Kruse, Thomas; Schneider, Judith C; Schweizer, Nikolaus
A toolkit for robust risk assessment using F-divergences
Management Science
2020
Herausgeber: INFORMS Inst. for Operations Res. and the Management Sciences4336.
Kruse, Thomas; Schneider, Judith; Schweizer, Nikolaus
A toolkit for robust risk assessment using F-divergences
Management Science, 67 (10)
2020
Herausgeber: INFORMS4335.
Wolf, Julian; Huber, Florian; Erochok, Nikita; Heinen, Flemming; Guérin, Vincent; Legault, Claude Y.; Huber, Stefan M.
Activation of a Metal‐Halogen Bond by Halogen Bonding
Angewandte Chemie International Edition, 59 (38) :16496–16500
2020
ISSN: 1433-7851, 1521-37734334.
Glück, Jochen; Weber, Martin R.
Almost interior points in ordered Banach spaces and the long-term behaviour of strongly positive operator semigroups
Studia Math., 254 (3) :237--263
20204333.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
Alternative Solarzellen mit Titandioxid - Ein Mentoring Projekt
MNU, 73 (2) :108--112
20204332.
Totzeck, Claudia
An anisotropic interaction model with collision avoidance
Kinetic and Related Models, 13 (6) :1219-1242
20204331.
Kruse, Thomas; Urusov, Mikhail
Approximating exit times of continuous Markov processes
Discrete and Continuous Dynamical Systems-B, 25 (9) :3631–3650
2020
Herausgeber: American Institute of Mathematical Sciences4330.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
BNE-Strukturen gemeinsam gestalten. Fachdidaktische Perspektiven und Forschungen zu Bildung für nachhaltige Entwicklung in der Lehrkräftebildung.
Band 13 aus Erziehungswissenschaft und Weltgesellschaft
Kapitel Chemiedidaktik als BNE-Multiplikator - Arbeitskreispraktika zur Erprobung von Schulversuchen und deren Reflexion hinsichtlich des BNE-Bezug., Seite 83-94
Herausgeber: Andreas Keil, Miriam Kuckuck und Mira Faßbender, Waxman, Münster
2020
83-94ISBN: 978-3-8309-4158-3
4329.
Bohrmann-Linde, Claudia; Kröger, Simone; Siehr (Hrsg.), Ilona
Chemie 2 - Gymnasium G9 NRW
Herausgeber: C.C.Buchner
20204328.
Bohrmann-Linde, Claudia; Kröger, Simone; Siehr (Hrsg.), Ilona
Chemie Gesamtband Sek I NRW
Herausgeber: C.C.Buchner
20204327.
Tausch, Michael W.
Chemie mit Licht - Innovative Didaktik für Studium und Lehre
Herausgeber: Springer Verlag
2020ISBN: 978-3-662-60376-5
4326.
Tiemann, Myrel; Clemens, Markus; Schmuelling, Benedikt
Comparison of Conventional and Magnetizable Concrete Core Designs in Wireless Power Transfer for Electric Vehicles
2020 {IEEE} {PELS} Workshop on Emerging Technologies: Wireless Power Transfer ({WoW})
Herausgeber: {IEEE}
November 20204325.
Totzeck, Claudia; Wolfram, Marie-Therese
Consensus-Based Global Optimization with Personal Best
Mathematical Biosciences and Engineering, 17 (5) :6026-6044
20204324.
Günther, Michael; Höllwiesera, Roman; Knechtli, Francesco
Constrained HMC algorithms for Gauge-Higgs models
, AIP Conference ProceedingsBand2293, Seite 290004
AIP Publishing LLC
20204323.
Günther, Michael; Höllwieser, Roman; Knechtli, Francesco
Constrained hybrid Monte Carlo algorithms for Gauge-Higgs models
Computer Physics Communications, 254 :107192
2020
Herausgeber: Elsevier4322.
Günther, Michael; Höllwieser, Roman; Knechtli, Francesco
Constrained hybrid Monte Carlo algorithms for Gauge-Higgs models
Computer Physics Communications, 254 :107192
2020
Herausgeber: Elsevier4321.
Günther, Michael; Höllwieser, Roman; Knechtli, Francesco
Constrained hybrid Monte Carlo algorithms for gauge-Higgs models
Computer Physics Communications, 254 :107192
2020
Herausgeber: North-Holland4320.
De Sterck, H.; Friedhoff, S.; Howse, A. J. M.; MacLachlan, S. P.
Convergence analysis for parallel-in-time solution of hyperbolic systems
Numer. Linear Algebra Appl., 27 (1) :e2271, 31
20204319.
De Sterck, H.; Friedhoff, S.; Howse, A. J. M.; MacLachlan, S. P.
Convergence analysis for parallel-in-time solution of hyperbolic systems
Numer. Linear Algebra Appl., 27 (1) :e2271, 31
20204318.
De Sterck, H.; Friedhoff, S.; Howse, A. J. M.; MacLachlan, S. P.
Convergence analysis for parallel-in-time solution of hyperbolic systems
Numer. Linear Algebra Appl., 27 (1) :e2271, 31
20204317.
Abel, Ulrich; Heilmann, Margareta; Kushnirevych, Vitaliy
Convergence of linking Baskakov-type operators
Periodica Mathematica Hungarica, 80 :280-288
2020
