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
5186.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 4 :100039
2023
Herausgeber: Elsevier5185.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep FDM: Enhanced finite difference methods by deep learning
Franklin Open, 4 :100039
2023
Herausgeber: Elsevier5184.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep finite difference method for solving Asian option pricing problems
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5183.
Kossaczká, Tatiana; Ehrhardt, Matthias; Günther, Michael
Deep finite difference method for solving Asian option pricing problems
Preprint IMACM
2023
Herausgeber: Bergische Universität Wuppertal5182.
Kapllani, Lorenc; Teng, Long
Deep Learning algorithms for solving high-dimensional nonlinear Backward Stochastic Differential Equations
Discrete Contin. Dyn. Syst. - B
2023
ISSN: 1531-34925181.
Kapllani, Lorenc; Teng, Long
Deep Learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations
Discrete Contin. Dyn. Syst. - B
20235180.
Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
20235179.
Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense
Preprint
20235178.
Ackermann, Julia; Jentzen, Arnulf; Kruse, Thomas; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense
Preprint
20235177.
Abdul Halim, Adila; others
Deep-Learning-Based Cosmic-Ray Mass Reconstruction Using the Water-Cherenkov and Scintillation Detectors of AugerPrime
PoS, ICRC2023 :371
20235176.
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: 2673-31615175.
Khosrawi-Rad, Bijan; Borchers, Arne; Grogorick, Linda; Robra-Bissantz, Susanne
Design Principles for Gamified Pedagogical Conversational Agents
Seite 67 - 82
Academic MindTrek Conference (MindTrek)
Tampere, Finnland
20235174.
Ehrhardt, Matthias; Matyokubov, Kh Sh
Driven transparent quantum graphs
Preprint
20235173.
Ehrhardt, Matthias; Matyokubov, Kh Sh
Driven transparent quantum graphs
Preprint
20235172.
Felpel, Mike; Kienitz, Jörg; McWalter, Thomas
Effective stochastic local volatility models
Quantitative Finance, 23 (12) :1731–1750
2023
Herausgeber: Routledge5171.
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}5170.
Di Persio, Luca; Ehrhardt, Matthias
Electricity price forecasting via statistical and deep learning approaches: The German case
AppliedMath, 3 (2) :316–342
2023
Herausgeber: MDPI5169.
Di Persio, Luca; Ehrhardt, Matthias
Electricity price forecasting via statistical and deep learning approaches: The German case
AppliedMath, 3 (2) :316–342
2023
Herausgeber: MDPI5168.
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 Institute5167.
Glück, Jochen; Hölz, Julian
Eventual cone invariance revisited
Linear Algebra and its Applications, 675 :274 - 293
20235166.
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/Heidelberg5165.
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 Press5164.
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 Press5163.
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
März 2023
Herausgeber: Academic Press5162.
Grogorick, Linda; Rohde, Moritz; Khosrawi-Rad, Bijan; Robra-Bissantz, Susanne
Fiction or Reality - Which Game Story Promotes Learning Outcome More?
Seite 441-456
36th Bled eConference Digital Economy and Society
Bled, Slowenien
2023
