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
4366.
Haack, Alexander; Polaczek, Christine; Tsolakis, Manuel; Thinius, Marco; Kersten, Hendrik; Benter, Thorsten
Charge Retention/Charge Depletion in ESI-MS: Theoretical Rationale
Journal of the American Society for Mass Spectrometry, 31 (4) :785-795
April 20204365.
Haack, Alexander; Polaczek, Christine; Tsolakis, Manuel; Thinius, Marco; Kersten, Hendrik; Benter, Thorsten
Charge Retention/Charge Depletion in ESI-MS: Theoretical Rationale
Journal of the American Society for Mass Spectrometry, 31 (4) :785-795
April 20204364.
Crouse, Jeff; Haack, Alexander; Benter, Thorsten; Hopkins, W. Scott
Understanding Nontraditional Differential Mobility Behavior: A Case Study of the Tricarbastannatrane Cation, N(CH \(_{2}\) CH \(_{2}\) CH \(_{2}\) ) \(_{3}\) Sn \(^{+}\)
Journal of the American Society for Mass Spectrometry, 31 (4) :796-802
April 20204363.
Crouse, Jeff; Haack, Alexander; Benter, Thorsten; Hopkins, W. Scott
Understanding Nontraditional Differential Mobility Behavior: A Case Study of the Tricarbastannatrane Cation, N(CH \(_{2}\) CH \(_{2}\) CH \(_{2}\) ) \(_{3}\) Sn \(^{+}\)
Journal of the American Society for Mass Spectrometry, 31 (4) :796-802
April 20204362.
Crouse, Jeff; Haack, Alexander; Benter, Thorsten; Hopkins, W. Scott
Understanding Nontraditional Differential Mobility Behavior: A Case Study of the Tricarbastannatrane Cation, N(CH 2 CH 2 CH 2 ) 3 Sn +
Journal of the American Society for Mass Spectrometry, 31 (4) :796-802
April 20204361.
Izak-Nau, Emilia; Campagna, Davide; Baumann, Christoph; Göstl, Robert
Polymer mechanochemistry-enabled pericyclic reactions
Polymer Chemistry, 11 (13) :2274--2299
März 2020
ISSN: 1759-99624360.
Haack, Alexander; Benter, Thorsten; Kersten, Hendrik
Computational analysis of the proton bound acetonitrile dimer, (ACN) \(_{2}\) H \(^{+}\)
Rapid Communications in Mass Spectrometry
März 20204359.
Haack, Alexander; Benter, Thorsten; Kersten, Hendrik
Computational analysis of the proton bound acetonitrile dimer, (ACN) \(_{2}\) H \(^{+}\)
Rapid Communications in Mass Spectrometry
März 20204358.
Haack, Alexander; Benter, Thorsten; Kersten, Hendrik
Computational analysis of the proton bound acetonitrile dimer, (ACN) 2 H +
Rapid Communications in Mass Spectrometry
März 20204357.
Sun, Jing; Su, Juanjuan; Ma, Chao; Göstl, Robert; Herrmann, Andreas; Liu, Kai; Zhang, Hongjie
Fabrication and Mechanical Properties of Engineered Protein-Based Adhesives and Fibers
Advanced Materials, 32 (6) :1906360
Februar 2020
ISSN: 1521-40954356.
[english] Meuter, Nico; Spinnen, Sebastian; Tausch, Michael W.
Two Versatile Experiments for Teaching Photochemistry: Photon Upconversion by TTA and All Optical INHIBIT Logical Gate
EPA (European Photochemistry Association) Newsletter (97) :9-15
Februar 20204355.
Stratigaki, Maria; Baumann, Christoph; Breemen, Lambert C. A. van; Heuts, Johan P. A.; Sijbesma, Rint P.; Göstl, Robert
Fractography of poly(N-isopropylacrylamide) hydrogel networks crosslinked with mechanofluorophores using confocal laser scanning microscopy
Polymer Chemistry, 11 (2) :358--366
Januar 2020
ISSN: 1759-99624354.
1-Nitrogen-Functionalized 2-Haloalkenes (Update 2020)
Science of Synthesis, Knowledge Updates (2) :235–275
20204353.
Budde, Christian; Farkas, B{\'a}lint
A {D}esch-{S}chappacher perturbation theorem for bi-continuous semigroups
Math. Nachr., 293 (6) :1053-1073
20204352.
Budde, Christian; Farkas, Bálint
A Desch-Schappacher perturbation theorem for bi-continuous semigroups
Math. Nachr., 293 (6) :1053-1073
20204351.
Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail; others
A functional limit theorem for coin tossing Markov chains
, Annales de l'Institut Henri Poincaré, Probabilités et StatistiquesBand56, Seite 2996--3019
Institut Henri Poincaré
20204350.
Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail; others
A functional limit theorem for coin tossing Markov chains
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 56 (4) :2996–3019
2020
Herausgeber: Institute of Mathematical Statistics4349.
Teng, Long; Lapitckii, Aleksandr; Günther, Michael
A multi-step scheme based on cubic spline for solving backward stochastic differential equations
Applied Numerical Mathematics, 150 :117–138
2020
Herausgeber: Elsevier4348.
Teng, Long; Lapitckii, Aleksandr; Günther, Michael
A multi-step scheme based on cubic spline for solving backward stochastic differential equations
Applied Numerical Mathematics, 150 :117--138
April 2020
Herausgeber: North-Holland4347.
Teng, Long; Lapitckii, Aleksandr; Günther, Michael
A multi-step scheme based on cubic spline for solving backward stochastic differential equations
Applied Numerical Mathematics, 150 :117–138
2020
Herausgeber: Elsevier4346.
Teng, Long; Wu, Xueran; Günther, Michael; Ehrhardt, Matthias
A new methodology to create valid time-dependent correlation matrices via isospectral flows
ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2) :361–371
2020
Herausgeber: EDP Sciences4345.
Teng, Long; Wu, Xueran; Günther, Michael; Ehrhardt, Matthias
A new methodology to create valid time-dependent correlation matrices via isospectral flows
ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2) :361–371
2020
Herausgeber: EDP Sciences4344.
Teng, Long; Wu, Xueran; Günther, Michael; Ehrhardt, Matthias
A new methodology to create valid time-dependent correlation matrices via isospectral flows
ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2) :361--371
Februar 2020
Herausgeber: EDP Sciences4343.
Teng, Long; Wu, Xueran; Günther, Michael; Ehrhardt, Matthias
A new methodology to create valid time-dependent correlation matrices via isospectral flows
ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2) :361–371
2020
Herausgeber: EDP Sciences4342.
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; Nguyen, Tuan Anh
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
SN Partial Differential Equations and Applications, 1 (2) :1--34
2020
Herausgeber: Springer International Publishing
