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
5356.
Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Positive linear operators preserving certain monomials on [0, ∞)
Dolomites Research Notes on Approximation, 16 :1-9
2023
ISSN: 2035-68035355.
Mittendorf, Fabia; Quambusch, Moritz; Kirsch, S. F.
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry, 2023 (21) :4574-4577
Mai 2023
Herausgeber: RSC5354.
Kraus, Konstantin; Klamroth, Kathrin; Stiglmayr, Michael
On the online path extension problem -- Location and routing problems in board games
20235353.
[german] Grandrath, Rebecca
CapCut – intuitive und vollständige Videobearbeitung
:1-2
2023
Herausgeber: Friedrich-Schiller-Universität Jena, Institut für Anorganische und Analytische Chemie5352.
Ehrhardt, Matthias
3D Modeling of sound field hologram of moving source in presence of internal waves causing horizontal refraction.
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5351.
Heldmann, Fabian; Berkhahn, Sarah; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
20235350.
Jäschke, Jens; Skrepek, Nathanael; Ehrhardt, Matthias
Mixed-dimensional geometric coupling of port-Hamiltonian systems
Applied Mathematics Letters, 137 :108508
2023
Herausgeber: Pergamon5349.
Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal optimization through multi-objective reformulation
European Journal of Operational Research, 311 (2) :427-443
2023
ISSN: 0377-22175348.
Heldmann, Fabian; Ehrhardt, Matthias; Klamroth, Kathrin
PINN training using biobjective optimization: The trade-off between data loss and residual loss
Journal of Computational Physics, 488 :112211
2023
Herausgeber: Academic Press5347.
Matyokubov, Kh Sh; Ehrhardt, Matthias
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
Physics Letters, Section A, 479 :128928
2023
Herausgeber: North-Holland5346.
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-Holland5345.
Ehrhardt, Matthias
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
2023
Herausgeber: Academic Press5344.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
Preprint IMACM
20235343.
Ehrhardt, Matthias
Use of interference patterns to control sound field focusing in shallow water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI5342.
Di Persio, Luca; Ehrhardt, Matthias
Electricity price forecasting via statistical and deep learning approaches: The German case
AppliedMath, 3 (2) :316–342
2023
Herausgeber: MDPI5341.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition
The Canadian Journal of Chemical Engineering, 101 (12) :7043–7052
2023
Herausgeber: John Wiley & Sons5340.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland5339.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 4 :100039
2023
Herausgeber: Elsevier5338.
Hilbig, André; Malzahn, Tamara; Losch, Daniel; Seifert, Christian; Weiß, Sabrina
starkeSeiten Informatik 7/8 Ausgabe Nordrhein-Westfalen ab 2021 - Schulbuch Klasse 7/8
Herausgeber: Klett Verlag
2023ISBN: 978-3-12-007534-9
5337.
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: MDPI5336.
Hilbig, André; Kohl, Matthias
Informatische Bildung für alle ermöglichen – Diversität und Inklusion im Pflichtfach Informatik begegnen
INFOS 2023 – 20. GI-Fachtagung Informatik und Schule
Würzburg
20235335.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
20235334.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep finite difference method for solving Asian option pricing problems
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5333.
Ehrhardt, Matthias; Kozitskiy, Sergey B
On a generalization of the split-step Padé method to the case of unknown vector-functions
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5332.
Bolten, Matthias; Donatelli, Marco; Ferrari, Paola; Furci, Isabella
Symbol based convergence analysis in multigrid methods for saddle point problems
Linear Algebra Appl., 671 :67--108
2023