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
4741.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
Foundations of Computational Mathematics, 22 (4) :905–966
2022
Herausgeber: Springer New York4740.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
Foundations of Computational Mathematics, 22 (4) :905--966
2022
Herausgeber: Springer US New York4739.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
Foundations of Computational Mathematics, 22 (4) :905–966
2022
Herausgeber: Springer New York4738.
Ballaschk, Frederic
Oxidations with Iodine(V) Compounds – From Stoichiometric Compounds to Catalysts
In Ishihara, Kazuaki and Muñiz, Kilian, Editor, Iodine Catalysis in Organic Synthesis
Seite 299–334
Herausgeber: Wiley
1 Edition
2022
299–3344737.
Zang, Martin; Haussmann, Norman; Mease, Robin; Stroka, Steven; Clemens, Markus; Burkert, Amelie; Popp, Alexander; Schmülling, Benedikt
Personenschutz bei induktivem Laden von Fahrzeugbatterien -- Ansätze zur praktikablen Echtzeitbestimmung der magneto-quasistatischen Körperexposition
In Proff, Heike, Editor
Seite 173--194
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2022
173--1944736.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
20224735.
Amin Zargaran, Uwe Janoske
Prediction of the mixing efficiency in rotor-stator system for high viscous mixtures based on a combined Lagrangian particle approach with an Immersed-Boundary Method
September 20224734.
Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor aus Mathematics in Industry
Herausgeber: Springer Cham
2022ISBN: 978-3-031-11817-3
4733.
Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor aus Mathematics in Industry
Herausgeber: Springer Cham
2022ISBN: 978-3-031-11817-3
4732.
Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor aus Mathematics in Industry
Herausgeber: Springer Cham
2022ISBN: 978-3-031-11817-3
4731.
Ehrhardt, Matthias; Günther, Michael
Progress in Industrial Mathematics at ECMI 2021
20224730.
Kääpä, Alex; Kampert, Karl-Heinz; Mayotte, Eric
Propagation of extragalactic cosmic rays in the Galactic magnetic field
PoS, EPS-HEP2021 :088
20224729.
Ankirchner, Stefan; Kruse, Thomas; Löhr, Wolfgang; Urusov, Mikhail
Properties of the EMCEL scheme for approximating irregular diffusions
Journal of Mathematical Analysis and Applications, 509 (1) :125931
2022
Herausgeber: Academic Press4728.
Ankirchner, Stefan; Kruse, Thomas; Löhr, Wolfgang; Urusov, Mikhail
Properties of the EMCEL scheme for approximating irregular diffusions
Journal of Mathematical Analysis and Applications, 509 (1) :125931
2022
Herausgeber: Academic Press4727.
Ankirchner, Stefan; Kruse, Thomas; Löhr, Wolfgang; Urusov, Mikhail
Properties of the EMCEL scheme for approximating irregular diffusions
Journal of Mathematical Analysis and Applications, 509 (1) :125931
2022
Herausgeber: Academic Press4726.
Haussmann, N.; Clemens, M.
Quantifizierung der Unsicherheit bei der Expositionsbestimmung des menschlichen Körpers durch niederfrequente Magnetfelder auf GPUs mit Monte-Carlo Simulationen
URSI e.V. Deutschland 2022 Kleinheubacher Tagung (KHB 2022)
Miltenberg, Germany
Herausgeber: Abstract accepted
20224725.
Kienitz, J.; McWalter, T. A.; Rudd, R.; Platen, E.
Quantization methods for stochastic differential equations
In Günther, Michael and Schilders, Wil, Editor aus Mathematics in Industry
Seite 299–329
Herausgeber: Springer Cham
2022
299–3294724.
Kienitz, J.; McWalter, T. A.; Rudd, R.; Platen, E.
Quantization methods for stochastic differential equations
In Günther, Michael and Schilders, Wil, Editor aus Mathematics in Industry
Seite 299–329
Herausgeber: Springer Cham
2022
299–3294723.
Addazi, A.; others
Quantum gravity phenomenology at the dawn of the multi-messenger era-A review
Prog. Part. Nucl. Phys., 125 :103948
20224722.
Reactions with Geminal Diazides: Long Known, Full of Surprises, and New Opportunities
Synthesis, 54 (20) :4447-4460
2022
Herausgeber: Thieme
ISSN: 0039-78814721.
Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :1--13
2022
Herausgeber: SpringerOpen4720.
Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :12
2022
Herausgeber: Springer Verlag4719.
Bannenberg, Marcus WFM; Ciccazzo, Angelo; Günther, Michael
Reduced order multirate schemes in industrial circuit simulation
Journal of Mathematics in Industry, 12 (1) :12
2022
Herausgeber: Springer Verlag4718.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems
arXiv preprint arXiv:2206.03772
20224717.
Rudd, Ralph; McWalter, Thomas; Kienitz, Jörg; Platen, Eckhard
Robust product Markovian quantization
The Journal of Computational Finance, 25 (4) :55–78
2022
Herausgeber: Incisive Media