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
- 2020
4241.
Berdysheva, Elena; Heilmann, Margareta; Hennings, Katharina
Pointwise convergence of the Bernstein-Durrmeyer operator with respect to a collection of measures
Journal of Approximation Theory, 251, Article 105339
20204240.
Arendt, Wolfgang; Glück, Jochen
Positive irreducible semigroups and their long-time behaviour
Philos. Trans. Roy. Soc. A, 378 (2185) :20190611, 17
20204239.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael; Ševčovič, Daniel
Pricing {American} Options with a Non-Constant Penalty Parameter
J. Risk Fin. Managem., 13 (6) :124
Juni 20204238.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael; Ševčovič, Daniel
Pricing American options with a non-constant penalty parameter
Journal of Risk and Financial Management, 13 (6) :124
2020
Herausgeber: MDPI4237.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael; Ševčovič, Daniel
Pricing American options with a non-constant penalty parameter
Journal of Risk and Financial Management, 13 (6) :124
2020
Herausgeber: MDPI4236.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael; Ševčovič, Daniel
Pricing American options with a non-constant penalty parameter
Journal of Risk and Financial Management, 13 (6) :124
2020
Herausgeber: MDPI4235.
Clevenhaus, Anna; Ehrhardt, Matthias; Günther, Michael; Ševčovič, Daniel
Pricing American options with a non-constant penalty parameter
Journal of Risk and Financial Management, 13 (6) :124
2020
Herausgeber: MDPI4234.
Schl\"uter, Felix; Gottowik, Marvin; Huege, Tim; Rautenberg, Julian
Refractive displacement of the radio-emission footprint of inclined air showers simulated with CoREAS
Eur. Phys. J. C, 80 (7) :643
20204233.
Farkas, Bálint; Kreidler, Henrik
Relative compactness of orbits and geometry of Banach spaces
J. Math. Anal. Appl
20204232.
Jacob, Birgit; Schwenninger, Felix; Vorberg, Lukas
Remarks on input-to-state stability of collocated systems with saturated feedback
Mathematics of Control, Signals, and Systems, 32 (3) :293-307
20204231.
Mittendorf, Fabia; Mohr, Fabian
Ring Expansion of 2-Azido-2-phenyl-indan-1,3-dione for the Generation of Heterocyclic Scaffolds
The Journal of Organic Chemistry, 85 (19) :12760–12769
2020
ISSN: 0022-3263, 1520-69044230.
Tong, My Linh; Leusch, Lena Theresa
Rubazonic Acids and Their Synthesis
The Journal of Organic Chemistry, 85 (9) :6008–6016
2020
ISSN: 0022-3263, 1520-69044229.
Putek, Piotr; Bartel, Andreas; Günther, Michael
Shape Optimization of a {PM} Synchronous Machine Under Probabilistic Constraints
Scientific Computing in Electrical Engineering: SCEE 2018, Taormina, Italy, September 2018 12, Seite 243--253
Springer International Publishing
20204228.
Putek, Piotr; Bartel, Andreas; Günther, Michael
Shape optimization of a PM synchronous machine under probabilistic constraints
In Nicosia, Giuseppe and Romano, Vittorio, Editor, Scientific Computing in Electrical Engineering: SCEE 2018, Taormina, Italy, September 2018ausMathematics in Industry, Seite 243–253
In Nicosia, Giuseppe and Romano, Vittorio, Editor
Herausgeber: Springer Cham
20204227.
Putek, Piotr; Bartel, Andreas; Günther, Michael
Shape optimization of a PM synchronous machine under probabilistic constraints
In Nicosia, Giuseppe and Romano, Vittorio, Editor, Scientific Computing in Electrical Engineering: SCEE 2018, Taormina, Italy, September 2018ausMathematics in Industry, Seite 243–253
In Nicosia, Giuseppe and Romano, Vittorio, Editor
Herausgeber: Springer Cham
20204226.
Putek, Piotr; Bartel, Andreas; Günther, Michael
Shape Optimization of a PM Synchronous Machine Under Probabilistic Constraints
Scientific Computing in Electrical Engineering: SCEE 2018, Taormina, Italy, September 2018 12, Seite 243--253
Springer International Publishing
20204225.
Pinnau, Rene; Totzeck, Claudia
Space mapping-based receding horizon control for stochastic interacting particle systems: dogs herding sheep
Journal of Mathematics in Industry, 10 (11)
20204224.
Durastante, Fabio; Furci, Isabella
Spectral analysis of saddle-point matrices from optimization problems with elliptic PDE constraints
Electron. J. Linear Algebra, 36 :773-798
20204223.
Durastante, Fabio; Furci, Isabella
Spectral analysis of saddle-point matrices from optimization problems with elliptic PDE constraints
Electron. J. Linear Algebra, 36 :773-798
20204222.
Durastante, Fabio; Furci, Isabella
Spectral analysis of saddle-point matrices from optimization problems with elliptic PDE constraints
Electron. J. Linear Algebra, 36 :773-798
20204221.
Glück, Jochen
Spectral gaps for hyperbounded operators
Adv. Math., 362 :106958, 24
20204220.
[german] Meuter, Nico; Spinnen, Sebastian; Yurdanur, Yasemin; Tausch, Michael W.
Spiropyran - ein didaktisches Multitalent - Experimentelle Erschließung chemischer Basiskonzepte mit dem molekularen Schalter Spiropyran/Merocyanin
CHEMKON, 27 (4) :169--178
20204219.
Jacob, Birgit; Möller, Sebastian; Wyss, Christian
Stability radius for infinite-dimensional interconnected systems
Systems Control Lett., 138 :Article ID 104662, 8 p.
20204218.
Ballaschk, Frederic; Özkaya, Yasemin
Stereocontrolled Synthesis of Harzialactone A and Its Three Stereoisomers by Use of Standardized Polyketide Building Blocks
European Journal of Organic Chemistry, 2020 (38) :6078–6080
2020
ISSN: 1434-193X, 1099-06904217.
Arendt, Wolfgang; ter Elst, Antonius F. M.; Glück, Jochen
Strict positivity for the principal eigenfunction of elliptic operators with various boundary conditions
Adv. Nonlinear Stud., 20 (3) :633--650
2020