Applied and Computational Mathematics (ACM)

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



2024

5243.

Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian systems’ modelling in electrical engineering
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor, Scientific Computing in Electrical Engineering: SCEE 2022, Amsterdam, The Netherlands, July 2022ausMathematics in Industry, Seite 133–143
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor
Herausgeber: Springer Cham
2024

5242.

Vinod, Vivin; Lyu, Dongyu; Ruth, Marcel; Kleinekathöfer, Ulrich; Schreiner, Peter R.; Zaspel, Peter
Predicting Molecular Energies of Small Organic Molecules with Multifidelity Methods.
2024

5241.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang-type trade execution problems to LQ stochastic control problems
Finance and Stochastics, 28 (3) :813–863
2024
Herausgeber: Springer Verlag

5240.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Reducing Obizhaeva-Wang-type trade execution problems to LQ stochastic control problems
Finance and Stochastics, 28 (3) :813–863
2024
Herausgeber: Springer Verlag

5239.

Saini, B. S.; Miettinen, K.; Klamroth, Kathrin; Steuer, R. E.; Dächert, Kerstin
SCORE Band Visualizations: Supporting Decision Makers in Comparing High-Dimensional Outcome Vectors in Multiobjective Optimization
IEEE Access, 12 :164371—164388
2024

5238.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands

5237.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands

5236.

Andersen, Kim Allan; Boomsma, Trine Krogh; Efkes, Britta; Forget, Nicolas
Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization
Management Science
2024

5235.

[english] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Simple biofuel cells: the superpower of baker’s yeast
Science in School - The European journal for science teachers, 66
Februar 2024

5234.

Wissdorf, Walter; Thinius, Marco; Benter, Thorsten
Simulation of Space Charge Effects in Fourier Transform Quadrupole Ion Traps (FT-QITs)
Journal of the American Society for Mass Spectrometry, 35 (12) :2969—2983
Dezember 2024
ISSN: 1044-0305, 1879-1123

5233.

Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov subspace methods: Matrix Sylvester equations
Math. Comp.
2024

5232.

Liu, Qian
Small-signal synchronization stability of sequence-decomposed grid-forming IBRs
Dezember 2024

5231.

Antunes, Carlos Henggeler; Fonseca, Carlos M.; Paquete, Luís; Stiglmayr, Michael
Special issue on exact and approximation methods for mixed-integer multi-objective optimization
Mathematical Methods of Operations Research
August 2024
Herausgeber: Springer Science and Business Media LLC
ISSN: 1432-5217

5230.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Spectral analysis of a class of linear hyperbolic partial differential equations
IEEE Control Systems Letters, 8 :766-771
2024

5229.

Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael; Marheineke, Nicole
Splitting Techniques for DAEs with port-Hamiltonian Applications
Preprint
2024

5228.

Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael; Marheineke, Nicole
Splitting Techniques for DAEs with port-Hamiltonian Applications
Preprint
2024

5227.

Bartel, A.; Diab, M.; Frommer, A.; G\"unther ; Marheineke, N.
Splitting Techniques for DAEs with port-Hamiltonian Applications
2024

5226.


Sprachsensibler Chemieunterricht digital umgesetzt - Ein Seminarexkurs im Rahmen des Praxissemesters
2024

5225.

Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
arXiv preprint arXiv:2401.17954
2024

5224.

Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
Preprint
2024

5223.

Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
Preprint
2024

5222.

Ackermann, Julia; Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems
Preprint
2024

5221.

Jacob, Birgit; Glück, Jochen; Meyer, Annika; Wyss, Christian; Zwart, Hans
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
J. Evol. Equ., 24 :Paper No. 62
2024

5220.

Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
Structural Aspects of Electromagneto-Quasistatic Field Formulations of Darwin-Type Derived in the Port-Hamiltonian System Framework
TechRxiv
2024
Herausgeber: IEEE

5219.

Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
Structural Aspects of Electromagneto-Quasistatic Field Formulations of Darwin-Type Derived in the Port-Hamiltonian System Framework
TechRxiv
2024
Herausgeber: IEEE