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



2025

5450.

Fan, Jilin; Lennarz, Regina; Zhang, Kuan; Mourran, Ahmed; Meisner, Jan; Xuan, Mingjun; Göstl, Robert; Herrmann, Andreas
Polymer microbubbles as universal platform to accelerate polymer mechanochemistry
Nature Communications, 16 (1) :5380
Juni 2025
ISSN: 2041-1723

5449.


Upcycling Food Waste: Ursolic Acid as Sustainable Feedstock
European Journal of Organic Chemistry
06 2025
ISSN: 1099-0690

5448.


Synthesis and Nucleophilic Ring-Opening of 1,1-Dicyanocyclopropanes: Accessing β-Aminocarbonyl Derivatives from Olefins
Organic Letters, 27 :5549-5554
05 2025
Herausgeber: ACS
ISSN: 1523-7052

5447.

Xu, Zhuo
Input-to-state type Stability for Simplified Fluid-Particle Interaction System
Mai 2025

5446.

Asya, Berçin V.; Wang, Sitao; Euchler, Eric; Khiêm, Vu Ngoc; Göstl, Robert
Optical Force Probes for Spatially Resolved Imaging of Polymer Damage and Failure
Aggregate, 6 (4) :e70014
April 2025
ISSN: 2692-4560

5445.

Hahmann, Johannes; Schüpp, Boris N.; Ishaqat, Aman; Selvakumar, Arjuna; Göstl, Robert; Gräter, Frauke; Herrmann, Andreas
Sequence-specific, mechanophore-free mechanochemistry of DNA
Chem, 11 (4) :102376
April 2025
ISSN: 2451-9294, 2451-9308

5444.

Ocqueteau, Vicente; Tucsnak, Marius
On an Initial Value Problem Describing the Small Oscillations of a Floating Cylinder
April 2025

5443.


Solid-Supported Iodine(V) Reagents in Organic Synthesis
Chemistry - A European Journal, 31 :e202500670
03 2025
Herausgeber: Wiley
ISSN: 1521-3765

5442.

[German] Grandrath, Rebecca; Wiebel, Michelle; Bensberg, Kathrin; Schebb, Nils Helge; Bohrmann-Linde, Claudia
Aus der Schale in die Schule
Nachrichten aus der Chemie, 73 (3) :10-12
März 2025

5441.

Storch, Sonja; Campagna, Davide; Aydonat, Simay; Göstl, Robert
Mechanochemical generation of nitrogen-centred radicals for the formation of tertiary amines in polymers
RSC Mechanochemistry, 2 (2) :240-245
März 2025

5440.


Aus der Schale in die Schule
Nachrichten aus der Chemie, 73 :10-12
02 2025
Herausgeber: Wiley
ISSN: 1868-0054

5439.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A Space Mapping approach for the calibration of financial models with the application to the Heston model
2025

5438.

Gaul, Daniela; Klamroth, Kathrin; Pfeiffer, Christian; Stiglmayr, Michael; Schulz, Arne
A Tight Formulation for the Dial-a-Ride Problem
European Journal of Operational Research, 321 (2) :363-382
2025
ISSN: 0377-2217

5437.

Könen, David; Stiglmayr, Michael
An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems
Discrete Applied Mathematics, 376 :1—14
2025
Herausgeber: Elsevier BV
ISSN: 0166-218X

5436.

Frommer, Andreas; Rinelli, Michele; Schweitzer, Marcel
Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices
Math. Comp., 94 :801-823
2025

5435.

Hoffe, Leon; Ulutas, Berna; Klamroth, Kathrin; Bracke, Stefan
Assessing the effectiveness and efficiency of selected solution approaches for two-dimensional stock cutting problems (Part III): Hybrid Approach For Printed Circuit Boards
AUTOMATION 2025: Conference on Automation — Innovations and Future Perspectives
2025

5434.

Kiesling, Elisabeth; Bohrmann-Linde, Claudia
Carbon Capture and Storage - Nachweis von adsorbiertem Kohlenstoffdioxid
Naturwissenschaften im Unterricht Chemie, 1/25 :Versuchskarteikarte
Februar 2025

5433.

Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Constructing Optimal Star Discrepancy Sets
accepted in Proceedings of the AMS
2025

5432.

Kunze, Markus; Mui, Jonathan; Ploss, David
Elliptic operators with non-local Wentzell-Robin boundary conditions
2025

5431.

Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning
Neural Network, 181
Januar 2025

5430.

Kienitz, J; Moodliyar, L
Gaussian views explained
Wilmott, 2025 (135) :72–77
2025
Herausgeber: Wilmott Magazine

5429.

Xu, Zhuo; Tucsnak, Marius
Global Exponential Stabilization for a Simplified Fluid-Particle Interaction System
Januar 2025

5428.

Bartel, Andreas; Schaller, Manuel
Goal-oriented time adaptivity for port-Hamiltonian systems
Journal of Computational and Applied Mathematics, 461 :116450
2025
ISSN: 0377-0427

5427.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-4655

5426.

Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
Computer Physics Communications, 309 :109478
2025
ISSN: 0010-4655