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



2020

4217.

Arendt, Wolfgang; ter Elst, Antonius F. M.; Glück, Jochen
Strict positivity for the principal eigenfunction of elliptic operators with various boundary conditions
Adv. Nonlinear Stud., 20 (3) :633--650
2020

4216.

Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Strong converse results for linking operators and convex functions
Journal of Function Spaces, 2020 (1) :4049167
2020

4215.

Bunker, P. R.; Jensen, Per
The Planck constant of action h\(_{A}\)
Journal of Quantitative Spectroscopy and Radiative Transfer
2020

4214.

Bunker, P. R.; Jensen, Per
The Planck constant of action h\(_{A}\)
Journal of Quantitative Spectroscopy and Radiative Transfer
2020

4213.

Bunker, P. R.; Jensen, Per
The Planck constant of action hA
Journal of Quantitative Spectroscopy and Radiative Transfer
2020

4212.

Kreidler, Henrik
The primitive spectrum of a semigroup of {M}arkov operators
Positivity, 24 (2) :287--312
2020

4211.

Kreidler, Henrik
The primitive spectrum of a semigroup of Markov operators
Positivity, 24 (2) :287--312
2020

4210.

Farkas, Bálint; Kreidler, Henrik
Towards a Koopman theory for dynamical systems on completely regular spaces
Phil. Trans. Royal Soc. A, 378
2020

4209.

Günther, Christoph; Günther, Michael; Günther, Daniel
Tracing contacts to control the COVID-19 pandemic
Preprint
2020

4208.

Günther, Christoph; Günther, Michael; Günther, Daniel
Tracing contacts to control the COVID-19 pandemic
arXiv preprint arXiv:2004.00517
2020

4207.

Günther, Christoph; Günther, Michael; Günther, Daniel
Tracing contacts to control the COVID-19 pandemic
Preprint
2020

4206.


Transparent boundary conditions for the sine-Gordon equation
2020

4205.

Ehrhardt, Matthias
Valuation of basket credit default swaps under stochastic default intensity models
Advances in Applied Mathematics and Mechanics, 12 (5) :1301–1326
2020
Herausgeber: Global Science Press

4204.

Ehrhardt, Matthias
Valuation of basket credit default swaps under stochastic default intensity models
Advances in Applied Mathematics and Mechanics, 12 (5) :1301–1326
2020
Herausgeber: Global Science Press

4203.

Ehrhardt, Matthias
Valuation of basket credit default swaps under stochastic default intensity models
Advances in Applied Mathematics and Mechanics, 12 (5) :1301--1326
2020
Herausgeber: Global Science Press

4202.

Tausch, Michael W.
Videoclip oder Realexperiment?
Nachrichten aus der Chemie, 68 (6-7) :18-19
2020

4201.

Skrepek, Nathanael
Well-posedness of linear first order Port-Hamiltonian Systems on multidimensional spatial domains
Evolution Equation \& Control Theory
2020

4200.

Ehrhardt, Matthias
Wide-angle mode parabolic equations for the modelling of horizontal refraction in underwater acoustics and their numerical solution on unbounded domains
Journal of Sound and Vibration, 484 :115526
2020
Herausgeber: Academic Press

4199.

Ehrhardt, Matthias
Wide-angle mode parabolic equations for the modelling of horizontal refraction in underwater acoustics and their numerical solution on unbounded domains
Journal of Sound and Vibration, 484 :115526
2020
Herausgeber: Academic Press

4198.

Ehrhardt, Matthias
Wide-angle mode parabolic equations for the modelling of horizontal refraction in underwater acoustics and their numerical solution on unbounded domains
Journal of Sound and Vibration, 484 :115526
2020
Herausgeber: Academic Press
2019

4197.

Yildiz, Deniz; Baumann, Christoph; Mikosch, Annabel; Kuehne, Alexander J. C.; Herrmann, Andreas; Göstl, Robert
Anti-Stokes Stress Sensing: Mechanochemical Activation of Triplet–Triplet Annihilation Photon Upconversion
Angewandte Chemie International Edition, 58 (37) :12919-12923
September 2019
ISSN: 1521-3773

4196.

Yildiz, Deniz; Baumann, Christoph; Mikosch, Annabel; Kuehne, Alexander J. C.; Herrmann, Andreas; Göstl, Robert
Anti-Stokes-Belastungsanzeige: Mechanochemische Aktivierung der Triplett-Triplett-Annihilierung-Photonen-Hochkonversion
Angewandte Chemie, 131 (37) :13051-13055
September 2019
ISSN: 1521-3757

4195.

Jensen, Per
Linear and bent triatomic molecules are not qualitatively different!
Canadian Journal of Physics
August 2019

4194.

Jensen, Per
Linear and bent triatomic molecules are not qualitatively different!
Canadian Journal of Physics :1-6
August 2019
Herausgeber: NRC Research Press

4193.

Jensen, Per
Linear and bent triatomic molecules are not qualitatively different!
Canadian Journal of Physics :1-6
August 2019
Herausgeber: NRC Research Press