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



5555

5600.

Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
Approximate and Weighted Data Reconstruction Attack in Federated Learning
IEEE Transactions on Big Data
5555
2026

5599.

Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
Journal of Mathematical Analysis and Applications
November 2026

5598.

Gao, Xiang; Chakraborty, Gurudas; Urhahne, Felix Joel; Lantzius-Beninga, Marcus; Lennarz, Regina; Fan, Jilin; Stappert, Kara; Meisner, Jan; Göstl, Robert; Herrmann, Andreas
The mechanochemical activation of a pyrimidine dimer
Chemical Science, 17 (21) :10589-10599
Juni 2026
Herausgeber: The Royal Society of Chemistry
ISSN: 2041-6539

5597.

Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
Journal of Differential Equations
Juni 2026

5596.

Xu, Zhuo
Input-to-state type Stability for Simplified Fluid-Particle Interaction System
IMA Journal of Mathematical Control and Information, 43 (3)
März 2026

5595.

Kiesling, Elisabeth; Grandrath, Rebecca; Bohrmann-Linde, Claudia
Von der Querschnittsaufgabe BNE zur Unterrichtsplanung: Ein Umsetzungsbeispiel zum Thema Fette für den Chemieunterricht der Sekundarstufe II
MNU-Journal, 02/2026 :141-146
März 2026

5594.

Kunze, Markus; Mui, Jonathan; Ploss, David
Elliptic operators with non-local Wentzell-Robin boundary conditions
Journal of Spectral Theory
Februar 2026

5593.

Barmin, Roman A.; Moosavifar, MirJavad; Rama, Elena; Blöck, Julia; Rix, Anne; Petrovskii, Vladislav S.; Gumerov, Rustam A.; Köhler, Jens; Pohl, Michael; Bastard, Céline; Rütten, Stephan; Charlton, Laura; Khiêm, Vu Ngoc; Domenici, Fabio; Lisson, Thomas; Savina, Ekaterina; Zhang, Rui; Baier, Jasmin; Koletnik, Susanne; Koutsos, Vasileios; Itskov, Mikhail; Paradossi, Gaio; Schmitz, Georg; Vermonden, Tina; De Laporte, Laura; Göstl, Robert; Herrmann, Andreas; Potemkin, Igor I.; Kiessling, Fabian; Lammers, Twan; Pallares, Roger M.
Microbubble Shell Stiffness Engineering Enhances Ultrasound Imaging, Drug Delivery, and Sonoporation
Advanced Materials, 38 (6) :e07655
Januar 2026
ISSN: 1521-4095

5592.

Tapera, Michael; Savvidis, Athanasios; Meysing, Cedric; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidative Cleavage of β-Substituted Primary Alcohols in Flow
Organic Letters
Januar 2026
Herausgeber: ACS
ISSN: 1523-7052

5591.

Prinz, Kathrin; Nemesch, Levin; Ruzika, Stefan
A High-Performance Parallel Algorithm for Multi-Objective Integer Optimization
2026

5590.

Ocqueteau, Vicente
Analysis of a Model for a Floating Platform Coupled with a Flexible Beam
2026

5589.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic expansions for generalized Bernstein-Durrmeyer and genuine Bernstein-Durrmeyer operators
Complex Anal. Oper. Theory, 20
2026

5588.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic properties for a general class of Szász-Mirakjan-Durrmeyer operators
Mathematical Methods in the Applied Sciences :734–743
2026

5587.

Elghazi, Bouchra; Jacob, Birgit; Zwart, Hans
Boundary control systems on a one-dimension spatial domain
2026

5586.

Sinani, Mario A.; Palacios, Rafael; Fasel, Urban; Wynn, Andrew
Data-Driven Parametric Aeroelastic Modeling of the Pazy Wing
Seite 0187
2026
0187

5585.

Finster, Rebecca; Grogorick, Linda; Robra-Bissantz, Susanne
Einheitliche Vorgaben, heterogene Praxis: Potenziale der NIS2-Umsetzung in einer öffentlichen Verwaltung
HMD - Praxis der Wirtschaftsinformatik
2026

5584.

Abel, Ulrich; Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Genuine Bernstein-Durrmeyer operators preserving 1 and x^j (II)
Approximation Theory and Special Functions, Seite 97--112
ATSF 2024
Ankara, Turkey
Herausgeber: Springer Nature Switzerland
2026

ISBN: 978-3-031-93279-3

5583.

Vinod, Vivin; Zaspel, Peter
Improvise, Adapt, Overcome: An On-The-Fly Multifidelity Algorithm for Efficient Machine Learning
2026

5582.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Kernels for composition of positive linear operators
Journal of Mathematical Analysis and Applications, 555 (2) :130052
2026
ISSN: 0022-247X

5581.

Zeller, Diana; Bohrmann-Linde, Claudia
KI-Chatbots als Unterrichtswerkzeug: Eine Lehrkräftefortbildung zum Einsatz von KI-Chatbots im Chemieunterricht
CHEMKON, 33/3 :71-76
2026
angenommen

5580.

Vinod, Vivin; Zaspel, Peter
LFaB: Low Fidelity as Bias for Active Learning in the Chemical Configuration Space
J. Chem. Theory Comput.
2026

5579.

Könen, David; Stiglmayr, Michael
Output-sensitive Complexity of Multi-Objective Integer Network Flow Problems
Journal of Combinatorial Optimization, 51 (14)
2026

5578.

Yuden, Kezang; Nemesch, Levin; Ruzika, Stefan
Parametric Biobjective Linear Programming
2026

5577.

Lopes, Gonçalo; Klamroth, Kathrin; Paquete, Luís
Solving hypervolume scalarizations for MOCO problems
2026

5576.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Convergence of linking Durrmeyer type modifications of generalized Baskatov operators
Bulleting of the Malaysian Math. Sciences Society