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



2018

3866.

Putek, Piotr; Janssen, Rick; Niehof, Jan; Maten, E. Jan W.; Pulch, Roland; Tasic, Bratislav; Günther, Michael
Nanoelectronic COupled problems solutions: Uncertainty quantification for analysis and optimization of an RFIC interference problem
Journal of Mathematics in Industry, 8 (1) :1–19
2018
Herausgeber: Springer Verlag

3865.

Putek, Piotr; Janssen, Rick; Niehof, Jan; Maten, E. Jan W.; Pulch, Roland; Tasic, Bratislav; Günther, Michael
Nanoelectronic COupled problems solutions: Uncertainty quantification for analysis and optimization of an RFIC interference problem
Journal of Mathematics in Industry, 8 (1) :1–19
2018
Herausgeber: Springer Verlag

3864.

Putek, P.; Janssen, R.; Niehof, J.; Maten, E. J. W.; Pulch, R.; Tasic, B.; Günther, M.
Nanoelectronic Coupled Problems Solutions: Uncertainty quantification of {RFIC} interference
In Quintela, P. and Barral, P. and Gómez, D. and Pena, F.J. and Rodríguez, J. and Salgado, P. and Vázquez-Mendéz, M.E., Editor, Progress in Industrial Mathematics at ECMI 2016 Band 26 aus Mathematics in Industry
Seite 271--279
Herausgeber: Springer
2018
271--279

3863.

Putek, Piotr; Janssen, Rick; Niehof, Jan; Maten, E. Jan W.; Pulch, Roland; Tasic, Bratislav; Günther, Michael
Nanoelectronic coupled problems solutions: Uncertainty quantification of RFIC interference
In Quintela, Peregrina and Barral, Patricia and Gómez, Dolores and Pena, Francisco J. and Rodríguez, Jerónimo and Salgado, Pilar and Vázquez-Mendéz, Miguel E., Editor, Progress in Industrial Mathematics at ECMI 2016ausMathematics in Industry, Seite 271–279
In Quintela, Peregrina and Barral, Patricia and Gómez, Dolores and Pena, Francisco J. and Rodríguez, Jerónimo and Salgado, Pilar and Vázquez-Mendéz, Miguel E., Editor
Herausgeber: Springer Cham
2018

3862.

Putek, Piotr; Janssen, Rick; Niehof, Jan; Maten, E. Jan W.; Pulch, Roland; Tasic, Bratislav; Günther, Michael
Nanoelectronic coupled problems solutions: Uncertainty quantification of RFIC interference
In Quintela, Peregrina and Barral, Patricia and Gómez, Dolores and Pena, Francisco J. and Rodríguez, Jerónimo and Salgado, Pilar and Vázquez-Mendéz, Miguel E., Editor, Progress in Industrial Mathematics at ECMI 2016ausMathematics in Industry, Seite 271–279
In Quintela, Peregrina and Barral, Patricia and Gómez, Dolores and Pena, Francisco J. and Rodríguez, Jerónimo and Salgado, Pilar and Vázquez-Mendéz, Miguel E., Editor
Herausgeber: Springer Cham
2018

3861.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices
Electron. Trans. Numer. Anal., 48 :362-372
2018

3860.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices
Electron. Trans. Numer. Anal., 48 :362-372
2018

3859.

Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices
Electron. Trans. Numer. Anal., 48 :362-372
2018

3858.

Gabbana, A.; Mendoza, M.; Succi, S.; Tripiccione, R.
Numerical evidence of electron hydrodynamic whirlpools in graphene samples
Computers & Fluids, 172 :644–650
2018
Herausgeber: Elsevier

3857.

Petrov, P.; Tyshchenko, A. G.; Ehrhardt, M.
Numerical solution of iterative parabolic equations approximating the nonlinear {Helmholtz} equation
Proceedings of the International Conference DAYS on DIFFRACTION 2018, St.Petersburg, Russia
2018

3856.

Ehrhardt, Matthias
Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation
2018 Days on Diffraction (DD), Seite 241–244
IEEE
Herausgeber: IEEE
2018

3855.

Ehrhardt, Matthias
Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation
2018 Days on Diffraction (DD), Seite 241--244
IEEE
2018

3854.

Ehrhardt, Matthias
Numerical solution of iterative parabolic equations approximating the nonlinear Helmholtz equation
2018 Days on Diffraction (DD), Seite 241–244
IEEE
Herausgeber: IEEE
2018

3853.

Ramadan, Leila
Offline-Pyrolyse GCxGC von Kunstoffpolymeren zur Analytik von Mikroplastik
2018

3852.

Ankirchner, Stefan; Klein, Maike; Kruse, Thomas; Urusov, Mikhail
On a certain local martingale in a general diffusion setting
2018

3851.

Bartel, Andreas; G\"unther, Michael
PDAEs in refined electrical network modeling
SIAM Review, 60 (1) :56--91
2018
Herausgeber: Society for Industrial and Applied Mathematics

3850.

Bartel, Andreas; Günther, Michael
PDAEs in refined electrical network modeling
SIAM Review, 60 (1) :56--91
Januar 2018
Herausgeber: Society for Industrial and Applied Mathematics

3849.

Bartel, Andreas; Günther, Michael
PDAEs in refined electrical network modeling
SIAM Review, 60 (1) :56–91
2018
Herausgeber: Society for Industrial and Applied Mathematics

3848.

Bartel, Andreas; Günther, Michael
PDAEs in refined electrical network modeling
SIAM Review, 60 (1) :56–91
2018
Herausgeber: Society for Industrial and Applied Mathematics

3847.

B{\'a}tkai, Andr{\'a}s; Jacob, Birgit; Voigt, Jürgen; Wintermayr, Jens
Perturbations of positive semigroups on {AM}-spaces
Semigroup Forum, 96 (2) :333--347
2018

3846.

Bátkai, András; Jacob, Birgit; Voigt, Jürgen; Wintermayr, Jens
Perturbations of positive semigroups on AM-spaces
Semigroup Forum, 96 (2) :333--347
2018

3845.

[english] Bohrmann-Linde, Claudia; Zeller, Diana
Photosensitizers for Photogalvanic Cells in the Chemistry Classroom
World Journal of Chemical Education, 6 (1) :36--42
2018
Herausgeber: Science and Education Publishing Co., Ltd.

3844.

[english] Tausch, Michael W.
Phototactive Thin Films in Science Education
World Journal of Chemical Education, 6 (1) :14--17
2018
Herausgeber: Science and Education Publishing Co., Ltd.

3843.

Bargetz, Christian; Wegner, Sven-Ake
Pivot duality of universal interpolation and extrapolation spaces
J. Math. Anal. Appl., 460 (1) :321--331
2018

3842.

Putek, Piotr; Maten, E Jan W; Günther, Michael; Bartel, Andreas
Preprint Shape optimization of machine under probabilistic constraints
2018