Applied and Computational Mathematics (ACM)

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 York

4740.

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 York

4739.

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 York

4738.

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
299–334

4737.

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--194

4736.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan; Seserman, Andra
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
2022

4735.

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 2022

4734.


Progress in Industrial Mathematics at ECMI 2021
In Ehrhardt, Matthias and Günther, Michael, Editor aus Mathematics in Industry
Herausgeber: Springer Cham
2022

ISBN: 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
2022

ISBN: 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
2022

ISBN: 978-3-031-11817-3

4731.

Ehrhardt, Matthias; Günther, Michael
Progress in Industrial Mathematics at ECMI 2021
2022

4730.

Kääpä, Alex; Kampert, Karl-Heinz; Mayotte, Eric
Propagation of extragalactic cosmic rays in the Galactic magnetic field
PoS, EPS-HEP2021 :088
2022

4729.

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 Press

4728.

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 Press

4727.

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 Press

4726.

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
2022

4725.

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
299–329

4724.

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
299–329

4723.

Addazi, A.; others
Quantum gravity phenomenology at the dawn of the multi-messenger era-A review
Prog. Part. Nucl. Phys., 125 :103948
2022

4722.


Reactions with Geminal Diazides: Long Known, Full of Surprises, and New Opportunities
Synthesis, 54 (20) :4447-4460
2022
Herausgeber: Thieme
ISSN: 0039-7881

4721.

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: SpringerOpen

4720.

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 Verlag

4719.

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 Verlag

4718.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems
arXiv preprint arXiv:2206.03772
2022

4717.

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