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
- 2019
4042.
Wißdorf, Walter; Lorenz, Matthias; Brockmann, Klaus Josef; Benter, Thorsten
Systematic Ion Source Parameter Assessment by Automated Determination of the Distribution of Ion Acceptance (DIA) Using APLI
Journal of The American Society for Mass Spectrometry, 30 (7) :1262-1275
2019
Herausgeber: Journal of The American Society for Mass Spectrometry4041.
Wissdorf, Walter; Lorenz, Matthias; Brockmann, Klaus Josef; Benter, Thorsten
Systematic Ion Source Parameter Assessment by Automated Determination of the Distribution of Ion Acceptance (DIA) Using APLI
Journal of The American Society for Mass Spectrometry, 30 (7) :1262-1275
2019
Herausgeber: Journal of The American Society for Mass Spectrometry4040.
[english] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Teaching Sustainability in the Chemistry Classroom: Exploring Fuel Cells in Simple Hands-on Experiments with Hydrogen, Sugar and Alcohol
World Journal of Chemical Education, 7 (2) :172-178
2019
ISSN: 2375-16574039.
Janssen, Rick; Gillon, Renaud; Wieers, Aarnout; Deleu, Frederik; Guegnaud, Hervé; Reynier, Pascal; Schoenmaker, Wim; Maten, E. Jan W.
Test cases for power-MOS devices and RF-circuitry
In ter Maten, E. Jan W. and Brachtendorf, Hans-Georg and Pulch, Roland and Schoenmaker, Wim and De Gersem, Herbert, Editor aus Mathematics in Industry
Seite 459–485
Herausgeber: Springer Cham
2019
459–4854038.
Ehrhardt, Matthias; Günther, Michael
The 2D tree--grid method
Journal of Computational Finance
20194037.
Biallas, Phillip; Mensak, Tobias M.; Kunz, Kevin-Alexander
The Deazidoalkoxylation: Sequential Nucleophilic Substitutions with Diazidated Diethyl Malonate
The Journal of Organic Chemistry, 84 (3) :1654–1663
2019
ISSN: 0022-32634036.
Ferrari, Paola; Furci, Isabella; Hon, Sean; Mursaleen, Mohammad Ayman; Serra-Capizzano, Stefano
The eigenvalue distribution of special 2-by-2 block matrix-sequences with applications to the case of symmetrized Toeplitz structures
SIAM J. Matrix Anal. Appl., 40 (3) :1066-1086
20194035.
Ferrari, Paola; Furci, Isabella; Hon, Sean; Mursaleen, Mohammad Ayman; Serra-Capizzano, Stefano
The eigenvalue distribution of special 2-by-2 block matrix-sequences with applications to the case of symmetrized Toeplitz structures
SIAM J. Matrix Anal. Appl., 40 (3) :1066-1086
2019
ISSN: 0895-47984034.
Ferrari, Paola; Furci, Isabella; Hon, Sean; Mursaleen, Mohammad Ayman; Serra-Capizzano, Stefano
The eigenvalue distribution of special 2-by-2 block matrix-sequences with applications to the case of symmetrized Toeplitz structures
SIAM J. Matrix Anal. Appl., 40 (3) :1066-1086
2019
ISSN: 0895-47984033.
Kruse, Thomas; Schneider, Judith C; Schweizer, Nikolaus
The joint impact of F-divergences and reference models on the contents of uncertainty sets
Operations Research, 67 (2) :428--435
2019
Herausgeber: INFORMS4032.
Kruse, Thomas; Schneider, Judith; Schweizer, Nikolaus
The joint impact of F-divergences and reference models on the contents of uncertainty sets
Operations Research, 67 (2) :428–435
2019
Herausgeber: INFORMS4031.
Bunker, Philip R.; Mills, Ian M.; Jensen, Per
The Planck constant and its units
Journal of Quantitative Spectroscopy and Radiative Transfer, 237 :106594
20194030.
Bunker, Philip R.; Mills, Ian M.; Jensen, Per
The Planck constant and its units
Journal of Quantitative Spectroscopy and Radiative Transfer, 237 :106594
20194029.
Bunker, Philip R.; Mills, Ian M.; Jensen, Per
The Planck constant and its units
Journal of Quantitative Spectroscopy and Radiative Transfer, 237 :106594
20194028.
Ehrhardt, Matthias; Günther, Michael
The Two-Dimensional Tree--Grid Method
Journal of Computational Finance, Forthcoming
20194027.
Kossaczky, Igor; Ehrhardt, Matthias; Günther, Michael
The two-dimensional tree-grid method
Journal of Computational Finance, 23 (2) :29–57
2019
Herausgeber: Incisive Media4026.
Kossaczky, Igor; Ehrhardt, Matthias
The two-dimensional tree-grid method
JOURNAL OF COMPUTATIONAL FINANCE, 23 (2) :29--57
2019
Herausgeber: INCISIVE MEDIA HAYMARKET HOUSE, 28-29 HAYMARKET, LONDON, SW1Y 4RX, ENGLAND4025.
Kossaczky, Igor; Ehrhardt, Matthias; Günther, Michael
The two-dimensional tree-grid method
Journal of Computational Finance, 23 (2) :29–57
2019
Herausgeber: Incisive Media4024.
Kossaczky, Igor; Ehrhardt, Matthias; Günther, Michael
The two-dimensional tree-grid method
Journal of Computational Finance, 23 (2) :29–57
2019
Herausgeber: Incisive Media4023.
Palma-Cando, A.; Rendon-Enriquez, Ibeth; Tausch, Michael W.; Scherf, U.
Thin Functional Polymer Films by Electropolymerization
Nanomaterials, 9 (8) :1125
20194022.
[english] Kremer, Richard; Meuter, Nico; Tausch, Michael W.
Towards Artificial Photosynthesis - Promoting Microscale Photochemistry in Science Education
African Journal of Chemical Education, 9 (3) :120-134
20194021.
[english] Brunnert, Rainer; Yurdanur, Yasemin; Tausch, Michael W.
Towards Artificial Photosynthesis in Science Education
World Journal of Chemical Education, 7 (2) :33--39
2019
Herausgeber: Science and Education Publishing Co., Ltd.4020.
Mellor, Thomas M.; Yurchenko, Sergey N.; Mant, Barry P.; Jensen, Per
Transformation Properties under the Operations of the Molecular Symmetry Groups G\(_{36}\) and G\(_{36}\)(EM) of Ethane H\(_{3}\)CCH\(_{3}\)
Symmetry, 11 (7) :862
20194019.
Mellor, Thomas M.; Yurchenko, Sergey N.; Mant, Barry P.; Jensen, Per
Transformation Properties under the Operations of the Molecular Symmetry Groups G\(_{36}\) and G\(_{36}\)(EM) of Ethane H\(_{3}\)CCH\(_{3}\)
Symmetry, 11 (7) :862
20194018.
Mellor, Thomas M.; Yurchenko, Sergey N.; Mant, Barry P.; Jensen, Per
Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3
Symmetry, 11 (7) :862
2019
