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



2021

4441.

Sabirov, K.K.; Yusupov, J.R.; Aripov, M.M.; Ehrhardt, M.; Matrasulov, D.U.
Reflectionless propagation of {Manakov} solitons on a line: A model based on the concept of transparent boundary conditions
Phys. Rev. E, 103 (4) :043305
2021
Herausgeber: APS

4440.

Ehrhardt, Matthias
Reflectionless propagation of Manakov solitons on a line: A model based on the concept of transparent boundary conditions
Physical Review E, 103 (4) :043305
2021
Herausgeber: American Physical Society

4439.

Ehrhardt, Matthias
Reflectionless propagation of Manakov solitons on a line: A model based on the concept of transparent boundary conditions
Physical Review E, 103 (4) :043305
2021
Herausgeber: American Physical Society

4438.


Reflectionless propagation of Manakov solitons on a line: A model based on the concept of transparent boundary conditions
Physical Review E, 103 (4) :043305
2021
Herausgeber: American Physical Society

4437.

Acu, Ana-Maria; Gonska, Heiner; Heilmann, Margareta
Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render
2021

4436.

Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Results in Applied Mathematics
2021

4435.

Jacob, Birgit; Kaiser, Julia T.; Zwart, Hans
Riesz bases of port-Hamiltonian systems
SIAM J. Control Optim., 59 (6) :4646-4665
2021

4434.

Bartel, Andreas; Ehrhardt, Matthias; Günther, Michael
Rosenbrock--Wanner-Type Methods
2021

4433.


Rosenbrock-Wanner-Type Methods: Theory and Applications
In T. Jax and A. Bartel and M. Ehrhardt and M. Günther and G. Steinebach, Editor
Herausgeber: Springer
2021

ISBN: 978-3030768096

4432.


Rosenbrock-Wanner-Type Methods: Theory and Applications
In Jax, Tim and Bartel, Andreas and Ehrhardt, Matthias and Günther, Michael and Steinebach, Gerd, Editor aus Mathematics Online First Collections
Herausgeber: Springer Cham
2021

ISBN: 978-3-030-76809-6

4431.


Rosenbrock-Wanner-Type Methods: Theory and Applications
In Jax, Tim and Bartel, Andreas and Ehrhardt, Matthias and Günther, Michael and Steinebach, Gerd, Editor aus Mathematics Online First Collections
Herausgeber: Springer Cham
2021

ISBN: 978-3-030-76809-6

4430.


Rosenbrock-Wanner-Type Methods: Theory and Applications
In Jax, Tim and Bartel, Andreas and Ehrhardt, Matthias and Günther, Michael and Steinebach, Gerd, Editor aus Mathematics Online First Collections
Herausgeber: Springer Cham
2021

ISBN: 978-3-030-76809-6

4429.

Abreu, Pedro; others
Search for upward-going showers with the Fluorescence Detector of the Pierre Auger Observatory
PoS, ICRC2021 :1140
2021

4428.

Kähne, B.; Clemens, M.
Semi-Explicit Time Integration of a Reduced Magnetic Vector Potential Magneto-Quasistatic Field Formulation
The 12th International Symposium on Electric and Magnetic Fields (EMF 2021), Online Conference, 06.-08.07.2021. Abstract accepted.
2021

4427.

Erdogdu, Duygu; Wissdorf, Walter; Allers, Maria; Kirk, Ansgar T.; Kersten, Hendrik; Zimmermann, Stefan; Benter, Thorsten
Simulation of Cluster Dynamics of Proton-Bound Water Clusters in a High Kinetic Energy Ion-Mobility Spectrometer
Journal of the American Society for Mass Spectrometry, 32 (9) :2436--2450
September 2021
ISSN: 1044-0305, 1879-1123

4426.

Gaul, Daniela; Klamroth, Kathrin; Stiglmayr, Michael
Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph
In M. Müller-Hannemann and F. Perea, Editor, 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021) Band 96 aus Open Access Series in Informatics (OASIcs)
Seite 8:1-8:16
Herausgeber: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2021
8:1-8:16

4425.

Weissen, Jennifer; Goettlich, Simone; Totzeck, Claudia
Space mapping-based optimization with the macroscopic limit of interacting particle systems
Optimization and Engineering, online
2021

4424.

Arora, Sahiba; Glück, Jochen
Spectrum and convergence of eventually positive operator semigroups
Semigroup Forum, 103 (3) :791--811
2021

4423.

Glück, Jochen; Mironchenko, Andrii
Stability criteria for positive linear discrete-time systems
Positivity, 25 (5) :2029--2059
2021

4422.

Jacob, Birgit; Skrepek, Nathanael
Stability of the multidimensional wave equation in port-Hamiltonian modelling
60th IEEE Conference on Decision and Control (CDC), Seite 6188-6193
Austin
2021

4421.

Alves Junior, Antonio Augusto; others
Status of the novel CORSIKA 8 air shower simulation framework
PoS, ICRC2021 :284
2021

4420.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Stochastic Runge-Kutta--Munthe-Kaas methods in the modelling of perturbed rigid bodies
2021

4419.

Günther, Michael; Sandu, Adrian; Zanna, Antonella
Symplectic GARK methods for Hamiltonian systems
arXiv preprint arXiv:2103.04110
2021

4418.

Günther, Michael; Sandu, Adrian; Zanna, Antonella
Symplectic GARK methods for Hamiltonian systems
Preprint
2021

4417.

Günther, Michael; Sandu, Adrian; Zanna, Antonella
Symplectic GARK methods for Hamiltonian systems
Preprint
2021