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
online4788.
Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with
20224787.
Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal4786.
Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
Preprint IMACM
2022
Herausgeber: Bergische Universität Wuppertal4785.
Bartel, Andreas; Ehrhardt, Matthias
Lagrangian instabilities in thermal convection with stable temperature profiles
arXiv preprint arXiv:2205.03856
April 20224784.
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 Press4783.
Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press4782.
Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press4781.
Bartel, Andreas; Ehrhardt, Matthias
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953 :A5
2022
Herausgeber: Cambridge University Press4780.
[german] Tausch, Michael W.
LED statt Gasbrenner - Mehr Licht für nachhaltigen Chemieunterricht
Chemie in unserer Zeit, 56 (3/2022) :188–196
20224779.
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
20224778.
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: 0375-96014777.
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 Publishing4776.
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 Publishing4775.
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
20224774.
Jäschke, J.; Skrepek, N.; Ehrhardt, M.
Mixed-Dimensional Geometric Coupling of Port-{Hamiltonian} Systems
IMACM preprint 22/04
Februar 20224773.
Doganay, Onur Tanil; Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael; Totzeck, Claudia
Modeling Minimum Cost Network Flows With Port-Hamiltonian Systems
PAMM
2022
Herausgeber: Wiley4772.
Tordeux, Antoine; Totzeck, Claudia
Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems
20224771.
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 Press4770.
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 Press4769.
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 Press4768.
Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Herausgeber: Springer Netherlands4767.
Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :869–901
2022
Herausgeber: Springer Netherlands4766.
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--274765.
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