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
5080.
Mayotte, Eric William; others
Measurement of the mass composition of ultra-high-energy cosmic rays at the Pierre Auger Observatory
PoS, ICRC2023 :365
20235079.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Mit Lactase und Lactose zum elektrischen Strom - enzymatische Brennstoffzellen auf Filterpapierbasis für den Chemieunterricht.
CHEMKON, 30 (1) :37-41
Januar 20235078.
Jäschke, Jens; Skrepek, Nathanael; Ehrhardt, Matthias
Mixed-dimensional geometric coupling of port-Hamiltonian systems
Applied Mathematics Letters, 137 :108508
2023
Herausgeber: Pergamon5077.
Jäschke, Jens; Skrepek, Nathanael; Ehrhardt, Matthias
Mixed-dimensional geometric coupling of port-Hamiltonian systems
Applied Mathematics Letters, 137 :108508
2023
Herausgeber: Pergamon5076.
Jäschke, Jens; Skrepek, Nathanael; Ehrhardt, Matthias
Mixed-dimensional geometric coupling of port-Hamiltonian systems
Applied Mathematics Letters, 137 :108508
2023
Herausgeber: Pergamon5075.
Tyshchenko, Andrey; Kozitskiy, Sergey; Kazak, Mikhail; Petrov, Pavel
Modern methods of sound propagation modelling based on the expansion of acoustic fields over normal modes
Acoustical Physics (accepted, to appear in 2023), 69 (5)
Juni 20235074.
Rajkovic, Michelle; Benter, Thorsten; Wissdorf, Walter
Molecular Dynamics-Based Modeling of Ion-Neutral Collisions in an Open Ion Trajectory Simulation Framework
Journal of the American Society for Mass Spectrometry, 34 (10) :2156—2165
Oktober 2023
ISSN: 1044-0305, 1879-11235073.
Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective matroid optimization with ordinal weights
Discrete Applied Mathematics, 335 :104-119
2023
ISSN: 0166-218X5072.
Vinod, Vivin; Maity, Sayan; Zaspel, Peter; Kleinekathöfer, Ulrich
Multifidelity Machine Learning for Molecular Excitation Energies
J. Chem. Theory Comput., 19 (21) :7658-7670
20235071.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems
Preprint
20235070.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems
20235069.
Müller, Mats; Kemper, Svenja; Schlenkhoff, Andreas
Numerical modelling of the hydraulic capacity of grates inlets (OpenFOAM)
E-proceedings of the 40th IAHR World Congress in 2023 in Vienna, Austria.
20235068.
Ehrhardt, Matthias; Kozitskiy, Sergey B
On a generalization of the split-step Padé method to the case of unknown vector-functions
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5067.
Ehrhardt, Matthias; Kozitskiy, Sergey B
On a generalization of the split-step Padé method to the case of unknown vector-functions
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5066.
Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
Integral Equations and Operator Theory, 95 :Paper No. 15
20235065.
Soroking, Mikhail; Petrov, Pavel; Budyansky, Maxim; Fayman, Pavel; Didov, Alexandr; Golov, Alexandr; Morgunov, Yuri
On the effect of horizontal refraction caused by an anticyclonic eddy in the case of long-range sound propagation in the Sea of Japan
J. Marine Sci. Eng. , 11 (9)
Juni 20235064.
Kraus, Konstantin; Klamroth, Kathrin; Stiglmayr, Michael
On the online path extension problem -- Location and routing problems in board games
20235063.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Accepted at Numerische Mathematik
20235062.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York5061.
Bartel, Andreas; Günther, Michael; Jacob, Birgit; Reis, Timo
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numerische Mathematik, 155 (1-2) :1–34
2023
Herausgeber: Springer New York5060.
Bartel, A.; Günther, M.; Jacob, Birgit; Reis, T.
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
Numer. Math., 155 (1-2) :1-34
20235059.
Farkas, Bálint; Jacob, Birgit; Reis, Timo; Schmitz, Merlin
Operator splitting based dynamic iteration for linear infinite-dimensional port-Hamiltonian systems
20235058.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
arXiv preprint arXiv:2304.01766
20235057.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
20235056.
Frommer, Andreas; Günther, Michael; Liljegren-Sailer, Björn; Marheineke, Nicole
Operator splitting for port-Hamiltonian systems
Preprint
2023
