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
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--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
5–274764.
Bartel, Andreas; Günther, Michael
Multirate schemes—an answer of numerical analysis to a demand from applications
Novel Mathematics Inspired by Industrial Challenges
Seite 5--27
Herausgeber: Springer International Publishing Cham
2022
5--274763.
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
5–274762.
Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on {GPU}
JMI, 12 (5)
20224761.
Kapllani, Lorenc; Teng, Long
Multistep schemes for solving backward stochastic differential equations on GPU
Journal of Mathematics in Industry, 12 (1) :1–22
2022
Herausgeber: Springer Verlag4760.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-nume\-rical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
J. Energy Storage, 45 :103746
2022
Herausgeber: Elsevier4759.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Herausgeber: Elsevier4758.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Herausgeber: Elsevier4757.
Fatoorehchi, Hooman; Ehrhardt, Matthias
Numerical and semi-numerical solutions of a modified Thévenin model for calculating terminal voltage of battery cells
Journal of Energy Storage, 45 :103746
2022
Herausgeber: Elsevier4756.
4755.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215–228
2022
Herausgeber: IOS Press4754.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215–228
2022
Herausgeber: IOS Press4753.
Ehrhardt, Matthias
On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Herausgeber: IOS Press4752.
Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On intertwining of maxima of sum of translates functions with nonsingular kernels
Trudy Inst. Mat. Mekh. UrO RAN
20224751.
Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
20224750.
Petrov, {Pavel S.}; Ehrhardt, Matthias; Trofimov, {M. Yu.}
On the decomposition of the fundamental solution of the {Helmholtz} equation via solutions of iterative parabolic equations
Asymptotic Analysis, 126 (3-4) :215--228
2022
Herausgeber: IOS Press4749.
Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
On the speed of convergence of Picard iterations of BSDEs
Probability, Uncertainty and Quantitative Risk, 7 (2)
2022
Herausgeber: American Institute of Mathematical Sciences4748.
Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
On the speed of convergence of Picard iterations of BSDEs
Probability, Uncertainty and Quantitative Risk, 7 (2)
2022
Herausgeber: American Institute of Mathematical Sciences4747.
Hutzenthaler, Martin; Kruse, Thomas; Nguyen, Tuan Anh
On the speed of convergence of Picard iterations of BSDEs
Probability, Uncertainty and Quantitative Risk, 7 (2)
2022
Herausgeber: American Institute of Mathematical Sciences4746.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator Splitting Based Dynamic Iteration for Linear Port-{H}amiltonian Systems
arXiv preprint arXiv:2208.03574
20224745.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator Splitting Based Dynamic Iteration for Linear Port-Hamiltonian Systems
arXiv preprint arXiv:2208.03574
20224744.
Sudhoff, Julia
Ordinal costs in multi-objective combinatorial optimization
Dissertation
Dissertation
Bergische Universität Wuppertal
20224743.
[german] Banerji, Amitabh; Dörschelln, Jennifer; Schwarz, D.
Organische Leuchtdioden im Chemieunterricht
Chemie in unserer Zeit, 52 (1) :34-41
20224742.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Journal of Numerical Mathematics
2022
Herausgeber: De Gruyter
