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

4789.

Kaiser, Jennifer; Zeller, Diana; Bohrmann-Linde, Claudia
Kursbuch zum Brausetablettenversuch. Eine Lerneinheit des Konzepts KriViNat
Herausgeber: Chemiedidaktik, Bergische Universität Wuppertal
2022
online

4788.

Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with
2022

4787.

Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal

4786.

Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal

4785.

Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
arXiv preprint arXiv:2205.03856
April 2022

4784.

Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active {L}agrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press

4783.

Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press

4782.

Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press

4781.

Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press

4780.

[german] Tausch, Michael W.
LED statt Gasbrenner - Mehr Licht für nachhaltigen Chemieunterricht
Chemie in unserer Zeit, 56 (3/2022) :188–196
2022

4779.

Daners, Daniel; Glück, Jochen; Mui, Jonathan
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
Differential and Integral Equations, 9/10 :727-756
2022

4778.

others
Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
arXiv preprint arXiv:2206.01283, 479 :128928
Mai 2022
ISSN: 0375-9601

4777.

Bannenberg, Marcus WFM; Kasolis, Fotios; Günther, Michael; Clemens, Markus
Maximum entropy snapshot sampling for reduced basis modelling
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 41 (3) :954–966
2022
Herausgeber: Emerald Publishing

4776.

Bannenberg, Marcus WFM; Kasolis, Fotios; Günther, Michael; Clemens, Markus
Maximum entropy snapshot sampling for reduced basis modelling
COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 41 (3) :954–966
2022
Herausgeber: Emerald Publishing

4775.

Wahdan, Shayma
Measurements of observables sensitive to colour reconnection in $t\bar{t}$ events with the ATLAS detector at $\sqrt{s}$ = 13 TeV
Bergische Universitaet Wuppertal
2022

4774.

Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
Februar 2022

4773.

Doganay, Onur Tanil; Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael; Totzeck, Claudia
Modeling Minimum Cost Network Flows With Port-Hamiltonian Systems
PAMM
2022
Herausgeber: Wiley

4772.

Tordeux, Antoine; Totzeck, Claudia
Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems
2022

4771.

Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022
Herausgeber: Academic Press

4770.

Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022
Herausgeber: Academic Press

4769.

Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 507 (1) :125761
2022
Herausgeber: Academic Press

4768.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Herausgeber: Springer Netherlands

4767.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Herausgeber: Springer Netherlands

4766.

Bartel, Andreas; Günther, Michael
Multirate Schemes -- An Answer of Numerical Analysis to a Demand from Applications
In Michael Günther and Wil Schilders, Editor, Novel Mathematics Inspired by Industrial Challenges
Seite 5--27
Herausgeber: Springer
2022
5--27

4765.

Bartel, Andreas; Günther, Michael
Multirate schemes—an answer of numerical analysis to a demand from applications
In Günther, Michael and Schilders, Wil, Editor aus Mathematics in Industry
Seite 5–27
Herausgeber: Springer Cham
2022
5–27