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
- 2023
4991.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
20234990.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Preprint
20234989.
Schäfers, Kevin; Günther, Michael; Sandu, Adrian
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
20234988.
Synthesis and evaluation of radioiodinated estrogens for diagnosis and therapy of male urogenital tumours
Organic & Biomolecular Chemistry, 2023 (21) :3090-3095
2023
Herausgeber: RSC
ISSN: 1477-05394987.
Bolten, Matthias; Friedhoff, S.; Hahne, J.
Task graph-based performance analysis of parallel-in-time methods
Parallel Comput., 118 :103050
20234986.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension
arXiv preprint arXiv:2303.14735
20234985.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60 :35
20234984.
Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
20234983.
Meinert, Janning; Morej\'on, Leonel; Sandrock, Alexander; Eichmann, Björn; Kreidelmeyer, Jonas; Kampert, Karl-Heinz
The impact of a modified CMB photon density on UHECR propagation
PoS, ICRC2023 :322
20234982.
Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
20234981.
Guerreiro, Andreia P.; Klamroth, Kathrin; Fonseca, Carlos M.
Theoretical aspects of subset selection in multi-objective optimization
In Brockhoff, D. and Emmerich, M. and Naujoks, B. and Purshouse, R., Editor aus Natural Computing Series
Seite 213--239
Herausgeber: Springer
2023
213--2394980.
[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 20234979.
Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI4978.
Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI4977.
Bülow, Friedrich; Hahn, Yannik; Meyes, Richard; Meisen, Tobias; others
Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps
International Journal of Energy Research, 2023
2023
Herausgeber: Hindawi4976.
Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland4975.
Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland4974.
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters A :128611
2023
Herausgeber: North-Holland4973.
Lichtenberg, Nils; Lutz, Valerie; Jessen, Wilhelm; Klein, Andreas; Kurtenbach, Ralf; Villena, Guillermo; Kleffmann, Jörg
TunNOx – Entwicklung eines photokatalytischen Reaktors zur Reduktion von Stickoxiden in Straßentunneln
Immissionsschutz (3) :8
August 2023
ISSN: 1868-77764972.
David, Amelie; Stroka, Steven; Haussmann, Norman; Schmülling, Benedikt; Clemens, Markus
Überprüfung der elektromagnetischen Umweltverträglichkeit bei induktiver Ladung
In Proff, Heike and Clemens, Markus and Marrón, Pedro J. and Schmülling, Benedikt, Editor
Seite 143-180
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2023
143-1804971.
Dobrick, Alexander; Hölz, Julian; Kunze, Markus
Ultra Feller operators from a functional analytic perspective
20234970.
Wiesen, Peter; Illmann, Jan Niklas
Umweltchemie: Methan in der Atmosphäre
Nachrichten aus der Chemie, 71 (2) :70—73
Februar 2023
ISSN: 1439-9598, 1868-00544969.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Submitted to SIAM-ASA J. Uncertain. Quantif.
20234968.
Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
20234967.
Dobrick, Alexander; Hölz, Julian
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
2023
