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

4916.

Edeko, Nikolai; Kreidler, Henrik; Nagel, Rainer
A dynamical proof of the van der Corput inequality
Dynamical Systems, 37 :648-665
2022

4915.

Hermle, Patrick; Kreidler, Henrik
A Halmos-von Neumann theorem for actions of general groups
2022

4914.

Budde, Christian; Dobrick, Alexander; Glück, Jochen; Kunze, Markus
A monotone convergence theorem for strong Feller semigroups
2022

4913.

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 Publishing

4912.

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 Publishing

4911.

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 Publishing

4910.


A neural network enhanced weighted essentially non-oscillatory method for nonlinear degenerate parabolic equations
Physics of Fluids, 34 (2) :026604
2022
Herausgeber: AIP Publishing LLC

4909.

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
2022

4908.

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
2022

4907.

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
2022

4906.

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
2022

ISBN: 978-3-031-11817-3

4905.

Ehrhardt, Matthias
A Nonstandard Finite Difference Scheme for a Time-Fractional Model of Zika Virus Transmission
2022

4904.

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 Press

4903.

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 Press

4902.

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
2022

4901.

Glück, Jochen
A note on the spectrum of irreducible operators and semigroups
Proc. Amer. Math. Soc., 150 (1) :257--266
2022

4900.

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: 1424-8220

4899.

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 GmbH

4898.

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 GmbH

4897.

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 Cham

4896.

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 & Francis

4895.

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 & Francis

4894.

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 & Francis

4893.

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 & Francis

4892.

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