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

5064.

Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
SIAM J. Matrix Anal. Appl., 44 (3) :1321-1348
2023

DOI: 10.1137/23M1556708

5063.

Schweitzer, Marcel
Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds
SIAM J. Matrix Anal. Appl., 44 (3) :1321-1348
2023

DOI: 10.1137/23M1556708

5062.

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

DOI: 10.22323/1.444.0425

5061.

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

DOI: 10.22323/1.444.0442

5060.

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

DOI: 10.22323/1.424.0042

5059.

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

DOI: 10.48550/arXiv.2306.06481

5058.

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

DOI: 10.48550/arXiv.2311.16019

5057.

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

5056.

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

5055.

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

DOI: 10.1007/s00233-023-10347-0

5054.

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

5053.

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

5052.

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

5051.

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

5050.

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

5049.

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

5048.

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

5047.

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

5046.

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

5045.

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

DOI: 10.48550/arXiv.2301.02019

5044.

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

5043.

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

DOI: 10.48550/arXiv.2304.14077

5042.


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

Download

5041.

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

5040.

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