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
5489.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Motivieren mit (Teil-)Aufgaben zur Erklärvideoproduktion im Chemieunterricht
In Johannes Huwer, Timm Wilke, Amitabh Banerji, Editor, Band Progress in Digitalisation in Chemistry Education 2024. Digitales Lehren und Lernen an Hochschule und Schule im Fach Chemie
Seite 37-42
Herausgeber: Waxmann-Verlag, Münster New York
2025
37-42ISBN: 978-3-8188-0042-0
5488.
Finster, Rebecca; Grogorick, Linda; Robra-Bissantz, Susanne
Navigation im Cyberraum: Die NIS2-Umsetzung in der öffentlichen Verwaltung - mit KOMPASS und SEXTANT
Fachtagung Rechts- und Verwaltungsinformatik (RVI)
Hamburg
20255487.
Schweitzer, Marcel
Near instance optimality of the Lanczos method for Stieltjes and related matrix functions
SIAM J. Matrix Anal. Appl., 46 :1846-1865
20255486.
Bolten, Matthias; Doganay, Onur Tanil; Gottschalk, Hanno; Klamroth, Kathrin
Non-convex shape optimization by dissipative Hamiltonian flows
Engineering Optimization, 57 :384--403
20255485.
Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas
Nonlinear Monte Carlo Methods with Polynomial Runtime for Bellman Equations of Discrete Time High-Dimensional Stochastic Optimal Control Problems
Appl. Math. Optim., 91 (1) :26
20255484.
Könen, David; Stiglmayr, Michael
On Supportedness in Multi‐Objective Integer Linear Programming
Journal of Multi-Criteria Decision Analysis, 32 (3)
November 2025
Herausgeber: Wiley
ISSN: 1099-13605483.
Figueira, José Rui; Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff Santos, Julia
On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization
Operations Research Letters :107302
20255482.
Löhken, Lara; Stiglmayr, Michael
On the multiobjective cable-trench problem
Journal of Combinatorial Optimization, 49 (55)
20255481.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5480.
Lorenz, Jan; Zwerschke, Tom; Günther, Michael; Schäfers, Kevin
Operator splitting for coupled linear port-Hamiltonian systems
Applied Mathematics Letters, 160 :109309
2025
Herausgeber: Elsevier5479.
Könen, David; Stiglmayr, Michael
Output-sensitive Complexity of Multi-Objective Integer Network Flow Problems
Combinatorial Optimization
20255478.
Sinani, Mario; Wynn, Andrew; Palacios, Rafael
Physics-Informed Data-Driven Modelling of Nonlinear Aerodynamic Forces of the Pazy Wing
AIAA SciTech Forum, 6-10 January
01 20255477.
Vinod, Vivin; Lyu, Dongyu; Ruth, Marcel; R. Schreiner, Peter; Kleinekathöfer, Ulrich; Zaspel, Peter
Predicting Molecular Energies of Small Organic Molecules With Multi-Fidelity Methods
J. Comp. Chem., 46 (6) :e70056
20255476.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Schrader, Claudia
Produktion eigener VR-Lernsettings im Projekt FoPro-VR. Ein interdisziplinärer Lehransatz für die Lehramtsausbildung
In Mrohs, Lorenz; Franz, Julia; Herrmann, Dominik; Lindner, Konstantin; Staake, Thorsten, Editor, Digitales Lehren und Lernen an der Hochschule. Strategien - Bedingungen - Umsetzung
Seite 191-204
Herausgeber: transcript, Bielefeld
2025
191-204ISBN: 9783839471203
5475.
Khosrawi-Rad, Bijan; Keller, Paul; Benner, Dennis; Grogorick, Linda; Borchers, Arne; Janson, Andreas; Leimeister, Jan Marco; Robra-Bissantz, Susanne
Promoting Students’ Motivation in Language Education with Gamified Pedagogical Conversational Agents
Computers & Education, 238 :1–24
20255474.
Vinod, Vivin; Zaspel, Peter
QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules
Sci. Data, 12 (1) :202
2025
Herausgeber: Nature Publishing Group
ISSN: 2052-44635473.
Xue, Chaoyang; Chen, Hui; McGillen, Max R.; Su, Hang; Cheng, Yafang; Kleffmann, Jörg; Li, Guo; Cazaunau, Mathieu; Colomb, Aurélie; Sciare, Jean; DeWitt, Langley; Marchand, Nicolas; Sarda-Esteve, Roland; Petit, Jean-Eudes; Kukui, Alexandre
Role of Heterogeneous Reactions in the Atmospheric Oxidizing Capacity in Island Environments
Environmental Science & Technology, 59 (6) :3153—3164
Februar 2025
ISSN: 0013-936X, 1520-58515472.
Patel, Vivak; Maldonado, D Adrian; Melnichenko, Maksim; Pritchard, Nathaniel; Rao, Vishwas; Rebrova, Elizaveta; Sankararaman, Sriram; Schweitzer, Marcel
Scientific Applications Leveraging Randomized Linear Algebra
20255471.
Clément, François; Doerr, Carola; Klamroth, Kathrin; Paquete, Luís
Searching Permutations for Constructing Uniformly Distributed Point Sets
Proceedings of the National Academy of Sciences, 122 (14) :e2424464122
20255470.
Heintz, Chris; Kersten, Hendrik; Benter, Thorsten; Wissdorf, Walter
Signatures of Charged Droplets from ESI: A Statistical Analysis of Non-summed Mass Spectra Compared to APCI
Journal of the American Society for Mass Spectrometry, 36 (4) :839—849
April 2025
ISSN: 1044-0305, 1879-11235469.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
Numer. Linear Algebra Appl., 32 :e2596
20255468.
Liu, Qian; Yanchang, Zhang; Zuan, Wang; Wang, Miao; Zhao, Xiaowei
Small-signal stability of sequence-decomposed grid-forming IBRs with DC-link voltage dynamics
Februar 20255467.
Arora, Sahiba; Mui, Jonathan
Smoothing of operator semigroups under relatively bounded perturbations
20255466.
Santos, Daniela Dos; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the Multiobejctive Quasi-Clique Problem
European Journal of Operational Research, 323 :409—424
20255465.
Hamadi, Majed; Mahdavi-Amiri, Nezam; Schweitzer, Marcel
Splitting methods based on the nonzero diagonal pattern for computing matrix functions
2025