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

5379.

Schaefers, Kevin; Peardon, Michael
A modified Cayley transform for SU(3)
2024

5378.

Ehrhardt, Matthias
A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission
Mathematical Biosciences and Engineering, 21 (1) :924–962
2024
Herausgeber: AIMS Press

5377.

Ehrhardt, Matthias
A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission
Mathematical Biosciences and Engineering, 21 (1) :924–962
2024
Herausgeber: AIMS Press

5376.

Hölz, Julian
A Note on the Uniform Ergodicity of Dynamical Systems.
2024

5375.

Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A numerical study of the impact of variance boundary conditions for the Heston model
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Springer
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Herausgeber: Bergische Universität Wuppertal
2024

5374.

Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A numerical study of the impact of variance boundary conditions for the Heston model
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Springer
In Burnecki, K. and Szwabiński, J. and Teuerle, M., Editor
Herausgeber: Bergische Universität Wuppertal
2024

5373.

Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
A Port-Hamiltonian System Perspective on Electromagneto-Quasistatic Field Formulations of Darwin-Type
Preprint
2024

5372.

Clemens, Markus; Henkel, Marvin-Lucas; Kasolis, Fotios; Günther, Michael
A Port-Hamiltonian System Perspective on Electromagneto-Quasistatic Field Formulations of Darwin-Type
Preprint
2024

5371.

Hoang, Manh Tuan; Ehrhardt, Matthias
A second-order nonstandard finite difference method for a general Rosenzweig-MacArthur predator--prey model
Journal of Computational and Applied Mathematics :115752
2024
Herausgeber: Elsevier

5370.

Dächert, Kerstin; Fleuren, Tino; Klamroth, Kathrin
A simple, efficient and versatile objective space algorithm for multiobjective integer programming
Mathematical Methods of Operations Research, 100 :351—384
2024

5369.

Vinod, Vivin; Zaspel, Peter
Assessing Non-Nested Configurations of Multifidelity Machine Learning for Quantum-Chemical Properties
Machine Learning: Science and Technology, 5 (4) :045005
2024

5368.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and x^j
Mathematical Methods in the Applied Sciences, 47 (18) :13718-13733
2024

5367.

Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch & Bound with Scalarization-Based Information
Mathematical Methods of Operations Research
2024

5366.

Vinod, Vivin; Zaspel, Peter
Benchmarking Data Efficiency in Δ-ML and Multifidelity Models for Quantum Chemistry.
2024

5365.

Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE-Fortbildungsreihe für Lehrkräfte und Studierende in der Didaktik der Chemie
Herausgeber: Gemeinsamer Studienausschuss (GSA) in der School of Education an der Bergischen Universität Wuppertal
Newsletter Lehrer*innenbildung an der Bergischen Universität Wuppertal
2024

5364.

Klass, Friedemann; Bartel, Andreas; Gabbana, PD Alessandro
Boundary conditions for multi-speed lattice Boltzmann methods
2024

5363.

Bailo, Rafael; Barbaro, Alethea; Gomes, Susana N.; Riedl, Konstantin; Roith, Tim; Totzeck, Claudia; Vaes, Urbain
CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods
Journal of Open Source Software, 9 (98) :6611
2024
Herausgeber: The Open Journal

5362.

Fasi, Massimiliano; Gaudreault, Stéphane; Lund, Kathryn; Schweitzer, Marcel
Challenges in computing matrix functions
2024

5361.

Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195–208
2024
Herausgeber: Pergamon

5360.

Finster, Rebecca; Grogorick, Linda; Robra-Bissantz, Susanne
ChatGPT erzähl mir eine Geschichte: Die Verwandlung von Lernwelten durch KI-gestützte Erzählungen
DeLFI Fachtagung Bildungstechnologien
Fulda
2024

ISBN: 978-3-88579-255-0

5359.

Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Coarse-grid operator optimization in multigrid reduction in time for time-dependent Stokes and Oseen problems
Jpn. J. Ind. Appl. Math.
2024

5358.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Commutativity and spectral properties for a general class of Szász-Mirakjan-Durrmeyer operators
Advances in Operator Theory, 10 (1) :14
2024

5357.

Vorberg, Lukas; Jacob, Birgit; Wyss, Christian
Computing the Quadratic Numerical Range
Journal of Computational and Applied Mathematics :116049
2024

5356.

Klamroth, Kathrin; Stiglmayr, Michael; Totzeck, Claudia
Consensus-Based Optimization for Multi-Objective Problems: A Multi-Swarm Approach
Journal of Global Optimization
2024

5355.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London