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

5391.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 2024

5390.

Izak-Nau, Emilia; Niggemann, Louisa P.; Göstl, Robert
Brownian Relaxation Shakes and Breaks Magnetic Iron Oxide-Polymer Nanocomposites to Release Cargo
Small, 20 (4) :2304527
Januar 2024
ISSN: 1613-6829

5389.

[english] Wiebel, Michelle; Bensberg, Kathrin; Wende, Luca; Grandrath, Rebecca; Plitzko, Kathrin; Bohrmann-Linde, Claudia; Schebb, Nils Helge
Efficient and simple extraction protocol for triterpenic acids from apples
Journal of Chemical Education
April 2024
Herausgeber: American Chemical Society and Division of Chemical Education, Inc.

5388.

Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports
IFAC-PapersOnLine, 58(6) :280-285
Mai 2024

5387.

Kapllani, Lorenc; Teng, Long
{A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations}
2024

5386.

Ehrhardt, Matthias; Kozitskiy, Sergey B
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration :118304
2024
Herausgeber: Elsevier

5385.

Petrov, Pavel S.; Ehrhardt, Matthias; Kozitskiy, Sergey B.
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration, 577 :118304
2024
Herausgeber: Academic Press

5384.

Petrov, Pavel S.; Ehrhardt, Matthias; Kozitskiy, Sergey B.
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration, 577 :118304
2024
Herausgeber: Academic Press

5383.

Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics, 101 (9-10) :1094–1112
2024
Herausgeber: Taylor & Francis

5382.

Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics, 101 (9-10) :1094–1112
2024
Herausgeber: Taylor & Francis

5381.

Clevenhaus, Anna; Totzeck, Claudia; Ehrhardt, Matthias
A gradient-based calibration method for the Heston model
International Journal of Computer Mathematics
2024

5380.

Khosrawi-Rad, Bijan; Strohmann, Timo; Grogorick, Linda; Robra-Bissantz, Susanne
A Meta-Study on Design Knowledge for Virtual Reality in Collaborative Work
Pacific Asia Conference on Information Systems (PACIS)
Ho Chi Minh City, Vietnam
2024

5379.

Schäfers, Kevin; Peardon, Michael; Günther, Michael
A modified Cayley transform for SU (3)
Preprint
2024

5378.

Schäfers, Kevin; Peardon, Michael; Günther, Michael
A modified Cayley transform for SU (3)
Preprint
2024

5377.

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

5376.

Carslaw, Nicola; Bekö, Gabriel; Langer, Sarka; Schoemaecker, Coralie; Mihucz, Victor G.; Dudzinska, Marzenna; Wiesen, Peter; Nehr, Sascha; Huttunen, Kati; Querol, Xavier; Shaw, David
A new framework for indoor air chemistry measurements: Towards a better understanding of indoor air pollution
Indoor Environments, 1 (1) :100001
März 2024
ISSN: 29503620

5375.

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

5374.

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

5373.

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

5372.

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

5371.

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

5370.

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

5369.

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

5368.

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

5367.

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