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

7088.

Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
06 2024

7087.

Ballaschk, Frederic; Bensberg, Kathrin; Crone, Benedikt; Kirsch, S. F.; Menz, Helge
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC

7086.

Ishaqat, Aman; Hahmann, Johannes; Lin, Cheng; Zhang, Xiaofeng; He, Chuanjiang; Rath, Wolfgang H.; Habib, Pardes; Sahnoun, Sabri E. M.; Rahimi, Khosrow; Vinokur, Rostislav; Mottaghy, Felix M.; Göstl, Robert; Bartneck, Matthias; Herrmann, Andreas
In Vivo Polymer Mechanochemistry with Polynucleotides
Advanced Materials, 36 :2403752
Mai 2024
ISSN: 1521-4095

7085.

Fan, Jilin; Zhang, Kuan; Xuan, Mingjun; Gao, Xiang; Vinokur, Rostislav; Göstl, Robert; Zheng, Lifei; Herrmann, Andreas
High-Intensity Focused Ultrasound-Induced Disulfide Mechanophore Activation in Polymeric Nanostructures for Molecule Release
CCS Chemistry, 6
April 2024

7084.

Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 2024

7083.

Aydonat, Simay; Hergesell, Adrian H.; Seitzinger, Claire L.; Lennarz, Regina; Chang, George; Sievers, Carsten; Meisner, Jan; Vollmer, Ina; Göstl, Robert
Leveraging mechanochemistry for sustainable polymer degradation
Polymer Journal, 56 (4) :249--268
April 2024
ISSN: 1349-0540

7082.

Broschinski, Christian; Majer, Felix; He, Siyang; Kuehne, Alexander J. C.; Göstl, Robert
Mechanochemical Activation of Red-Light-Excited Triplet–Triplet Annihilation Photon Upconversion
ACS Applied Optical Materials
März 2024

7081.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Spectral analysis of a class of linear hyperbolic partial differential equations
03 2024

7080.

[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Band Chemie professionell unterrichten
Herausgeber: T. Palenta
Februar 2024

ISBN: 9783758478413

7079.

Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-3844

7078.

Hastir, Anthony; Jacob, Birgit; Zwart, Hans
Linear-Quadratic optimal control for boundary controlled networks of waves
02 2024

7077.

Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X

7076.

Bensberg, Kathrin; Savvidis, Athanasios; Ballaschk, Frederic; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-6539

7075.

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

7074.

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

7073.

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

7072.

Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports
2024

7071.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

7070.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

7069.

Calvo-Garrido, MC; Ehrhardt, M; V{\'a}zquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390

7068.

Ehrhardt, Matthias
Computerunterstützte Mathematik Zeiten

7067.

Ehrhardt, Matthias; Farkas, B{\'a}lint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes

7066.

Ehrhardt, M
Asymptotische Analysis Vorlesungszeiten

7065.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas
Operator Splitting and Multirate Schemes

7064.

Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer

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