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
4916.
Edeko, Nikolai; Kreidler, Henrik; Nagel, Rainer
A dynamical proof of the van der Corput inequality
Dynamical Systems, 37 :648-665
20224915.
Hermle, Patrick; Kreidler, Henrik
A Halmos-von Neumann theorem for actions of general groups
20224914.
Budde, Christian; Dobrick, Alexander; Glück, Jochen; Kunze, Markus
A monotone convergence theorem for strong Feller semigroups
20224913.
Ehrhardt, Matthias; Günther, Michael
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing4912.
Ehrhardt, Matthias; Günther, Michael
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing4911.
Ehrhardt, Matthias; Günther, Michael
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing4910.
A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing LLC4909.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-reflecting boundary condition for multispeed lattice Boltzmann methods
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021ausMathematics in Industry, Seite 447–453
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224908.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-reflecting boundary condition for multispeed lattice Boltzmann methods
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021ausMathematics in Industry, Seite 447–453
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224907.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-reflecting boundary condition for multispeed lattice Boltzmann methods
In Ehrhardt, Matthias and Günther, Michael, Editor, Progress in Industrial Mathematics at ECMI 2021ausMathematics in Industry, Seite 447–453
In Ehrhardt, Matthias and Günther, Michael, Editor
Herausgeber: Springer Cham
20224906.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A non-reflecting boundary condition for multispeed lattice Boltzmann methods
In M. Ehrhardt and M. Günther, Editor, Accepted at Progress in Industrial Mathematics at ECMI 2021
Herausgeber: Springer-Verlag, Berlin
2022ISBN: 978-3-031-11817-3
4905.
Ehrhardt, Matthias
A Nonstandard Finite Difference Scheme for a Time-Fractional Model of Zika Virus Transmission
20224904.
Treibert, Sarah; Brunner, Helmut; Ehrhardt, Matthias
A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics
Mathematical Biosciences and Engineering, 19 (2) :1213–1238
2022
Herausgeber: AIMS Press4903.
Treibert, Sarah; Brunner, Helmut; Ehrhardt, Matthias
A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics
Mathematical Biosciences and Engineering, 19 (2) :1213–1238
2022
Herausgeber: AIMS Press4902.
Treibert, Sarah; Brunner, Helmut; Ehrhardt, Matthias
A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics
Math. Biosci. Eng, 19 (2) :1213--1238
20224901.
Glück, Jochen
A note on the spectrum of irreducible operators and semigroups
Proc. Amer. Math. Soc., 150 (1) :257--266
20224900.
Zoller, Julian; Zargaran, Amin; Braschke, Kamil; Meyer, Jörg; Janoske, Uwe; Dittler, Achim
A Novel Apparatus for Simultaneous Laser-Light-Sheet Optical Particle Counting and Video Recording in the Same Measurement Chamber at High Temperature
Sensors, 22 (4)
2022
ISSN: 1424-82204899.
Ehrhardt, Matthias
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios
Advances in continuous and discrete models, 2022 (1) :1–27
2022
Herausgeber: Springer Science and Business Media Deutschland GmbH4898.
Ehrhardt, Matthias
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios
Advances in continuous and discrete models, 2022 (1) :1–27
2022
Herausgeber: Springer Science and Business Media Deutschland GmbH4897.
Ehrhardt, Matthias
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios
Advances in Continuous and Discrete Models, 2022 (1) :61
2022
Herausgeber: Springer International Publishing Cham4896.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78–94
2022
Herausgeber: Taylor & Francis4895.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78–94
2022
Herausgeber: Taylor & Francis4894.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78–94
2022
Herausgeber: Taylor & Francis4893.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A port-Hamiltonian formulation of coupled heat transfer
Mathematical and Computer Modelling of Dynamical Systems, 28 (1) :78--94
2022
Herausgeber: Taylor & Francis4892.
Jäschke, Jens; Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit
A Port-Hamiltonian Formulation of Coupled Heat Transfer
Math. Comput. Model. Dyn. Syst., 28 (1) :78-94
2022