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
5062.
Kowol, Philipp; Bargmann, Swantje; Görrn, Patrick; Wilmers, Jana
Delamination Behavior of Highly Stretchable Soft Islands Multi-Layer Materials
Applied Mechanics, 4 (2) :514--527
2023
ISSN: 2673-31615061.
Ehrhardt, Matthias; Matyokubov, Kh Sh
Driven transparent quantum graphs
Preprint
20235060.
Ehrhardt, Matthias; Matyokubov, Kh Sh
Driven transparent quantum graphs
Preprint
20235059.
Felpel, Mike; Kienitz, Jörg; McWalter, Thomas
Effective stochastic local volatility models
Quantitative Finance, 23 (12) :1731–1750
2023
Herausgeber: Routledge5058.
Klamroth, Kathrin; Lang, Bruno; Stiglmayr, Michael
Efficient Dominance Filtering for Unions and Minkowski Sums of Non-Dominated Sets
Computers and Operations Research
2023
Herausgeber: Elsevier {BV}5057.
Di Persio, Luca; Ehrhardt, Matthias
Electricity price forecasting via statistical and deep learning approaches: The German case
AppliedMath, 3 (2) :316–342
2023
Herausgeber: MDPI5056.
Di Persio, Luca; Ehrhardt, Matthias
Electricity price forecasting via statistical and deep learning approaches: The German case
AppliedMath, 3 (2) :316–342
2023
Herausgeber: MDPI5055.
Di Persio, Luca; Ehrhardt, Matthias
Electricity Price Forecasting via Statistical and Deep Learning Approaches: The German Case
AppliedMath, 3 (2) :316--342
2023
Herausgeber: Multidisciplinary Digital Publishing Institute5054.
Glück, Jochen; Hölz, Julian
Eventual cone invariance revisited
Linear Algebra and its Applications, 675 :274 - 293
20235053.
Janssen, Nils; Fetzer, Jana R; Grewing, Jannis; Burgmann, Sebastian; Janoske, Uwe
Experimental investigation of particle--droplet--substrate interaction
Experiments in Fluids, 64 (3) :44
2023
Herausgeber: Springer Berlin Heidelberg Berlin/Heidelberg5052.
Ehrhardt, Matthias
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
2023
Herausgeber: Academic Press5051.
Ehrhardt, Matthias
Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water
Journal of Sound and Vibration, 544 :117388
2023
Herausgeber: Academic Press5050.
Abdul Halim, Adila; others
Constraints on UHECR characteristics from cosmogenic neutrino limits with the measurements of the Pierre Auger Observatory
PoS, ICRC2023 :1520
20235049.
Halim, A. Abdul; others
Constraining the sources of ultra-high-energy cosmic rays across and above the ankle with the spectrum and composition data measured at the Pierre Auger Observatory
JCAP, 05 :024
20235048.
Kääpä, Alex; Kampert, Karl-Heinz; Becker Tjus, Julia
Flux predictions in the transition region incorporating the effects from propagation of cosmic rays in the Galactic magnetic field
EPJ Web Conf., 283 :03006
20235047.
Kordon, Florian; Stiglmayr, Michael; Maier, Andreas; Vicario, Celia Mart{\'{\i}}n; Pertlwieser, Tobias; Kunze, Holger
A principled representation of elongated structures using heatmaps
Scientific Reports, 13 (15253)
September 20235046.
Metzmacher, Andreas; Burgmann, Sebastian; Janoske, Uwe
$\mu$PIV measurements of the phase-averaged velocity distribution within wavy films
Experiments in Fluids, 64 (4) :81
2023
Herausgeber: Springer Berlin Heidelberg Berlin/Heidelberg5045.
Ehrhardt, Matthias
3D Modeling of sound field hologram of moving source in presence of internal waves causing horizontal refraction.
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5044.
Ehrhardt, Matthias
3D Modeling of sound field hologram of moving source in presence of internal waves causing horizontal refraction.
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5043.
Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
A characteristic boundary condition for multispeed lattice Boltzmann methods
Communications in Computational Physics, 33 (1) :101–117
2023
Herausgeber: Global Science Press5042.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition
The Canadian Journal of Chemical Engineering, 101 (12) :7043–7052
2023
Herausgeber: John Wiley & Sons5041.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition
The Canadian Journal of Chemical Engineering, 101 (12) :7043–7052
2023
Herausgeber: John Wiley & Sons5040.
Zargaran, Amin; Dolshanskiy, Wladislaw; Stepanyuk, Alexey; Pauer, Werner; Janoske, Uwe
A hybrid approach based on Lagrangian particles and immersed-boundary method to characterize rotor--stator mixing systems for high viscous mixtures
Chemical Engineering Journal, 473 :145062
2023
Herausgeber: Elsevier5039.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
Preprint IMACM
20235038.
Fatoorehchi, Hooman; Ehrhardt, Matthias
A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control
Preprint IMACM
2023
