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

2023

5016.

Alameddine, Jean-Marco; others
Simulating radio emission from air showers with CORSIKA 8
PoS, ICRC2023 :425
2023

DOI: 10.22323/1.444.0425

5015.

Alameddine, Jean-Marco; others
Simulations of cross media showers with CORSIKA 8
PoS, ICRC2023 :442
2023

DOI: 10.22323/1.444.0442

5014.

Giaccari, Ugo Gregorio; others
Simulations of the antenna response for the Auger Radio Detector
PoS, ARENA2022 :042
2023

DOI: 10.22323/1.424.0042

5013.

Schweitzer, Marcel
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
2023

DOI: 10.48550/arXiv.2306.06481

5012.

Schweitzer, Marcel
Sketched and truncated polynomial Krylov methods: Matrix Equations
2023

DOI: 10.48550/arXiv.2311.16019

5011.

Bond, Amelia M. H.; Frey, Markus M.; Kaiser, Jan; Kleffmann, Jörg; Jones, Anna E.; Squires, Freya A.
Snowpack nitrate photolysis drives the summertime atmospheric nitrous acid (HONO) budget in coastal Antarctica
Atmospheric Chemistry and Physics, 23 (9) :5533—5550
Mai 2023
ISSN: 1680-7324

DOI: 10.5194/acp-23-5533-2023

5010.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Some results for the inverse of a Bernstein–Schnabl type operator
Analysis and Mathematical Physics, 13 (1)
2023

DOI: 10.1007/s13324-022-00777-4

5009.

Mui, Jonathan
Spectral properties of locally eventually positive operator semigroups
Semigroup Forum, 106 :460-480
2023

DOI: 10.1007/s00233-023-10347-0

5008.

Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon

DOI: 10.1016/j.aml.2022.108464

5007.

Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon

DOI: 10.1016/j.aml.2022.108464

5006.

Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon

DOI: 10.1016/j.aml.2022.108464

5005.

Clemens, Markus; Günther, Michael
Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework
2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), Seite 1–1
Herausgeber: IEEE
2023

DOI: 10.1109/ICEAA57318.2023.10297842

5004.

Clemens, Markus; Günther, Michael
Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework
2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), Seite 1–1
Herausgeber: IEEE
2023

DOI: 10.1109/ICEAA57318.2023.10297842

5003.

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-Holland

DOI: 10.1016/j.apnum.2023.07.024

5002.

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-Holland

DOI: 10.1016/j.apnum.2023.07.024

5001.

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-Holland

DOI: 10.1016/j.apnum.2023.07.024

5000.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta–Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics
2023
ISSN: 0168-9274

DOI: https://doi.org/10.1016/j.apnum.2023.07.024

4999.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
2023

DOI: 10.48550/arXiv.2301.02019

4998.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems--a sensitivity-based approach
arXiv preprint arXiv:2301.02019
2023

4997.

Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
2023

DOI: 10.48550/arXiv.2304.14077

4996.


Studies on the improvement of the matching uncertainty definition in top-quark processes simulated with Powheg+Pythia 8
CERN, Geneva
2023

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4995.

Bolten, Matthias; Donatelli, M.; Ferrari, P.; Furci, I.
Symbol based convergence analysis in block multigrid methods with applications for Stokes problems
Appl. Numer. Math., 193 :109-130
2023

DOI: 10.1016/j.apnum.2023.07.016

4994.

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

DOI: 10.1016/j.laa.2023.04.016

4993.

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

DOI: 10.1016/j.laa.2023.04.016

4992.

Günther, Michael; Sandu, Adrian; Schäfers, Kevin; Zanna, Antonella
Symplectic GARK methods for partitioned Hamiltonian systems
2023