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



2021

4491.

Donatelli, Marco; Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano; Sesana, Debora
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2356, 20
2021

4490.

Donatelli, Marco; Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano; Sesana, Debora
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2356, 20
2021
ISSN: 1070-5325

4489.

Donatelli, Marco; Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano; Sesana, Debora
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2356, 20
2021
ISSN: 1070-5325

4488.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; others
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Partial Differential Equations and Applications, 2 (6) :1--31
2021
Herausgeber: Springer

4487.

Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas; others
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
Partial Differential Equations and Applications, 2 (6) :1–31
2021
Herausgeber: Springer International Publishing

4486.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4485.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4484.

Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix sequences
Electron. J. Linear Algebra, 37 :370-386
2021

4483.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential--algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Herausgeber: North-Holland

4482.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Herausgeber: North-Holland

4481.

Hachtel, Christoph; Bartel, Andreas; Günther, Michael; Sandu, Adrian
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
Journal of Computational and Applied Mathematics, 387 :112499
2021
Herausgeber: North-Holland

4480.

Günther, Michael; Sandu, Adrian
Multirate linearly-implicit GARK schemes
BIT Numerical Mathematics :1--33
2021
Herausgeber: Springer Netherlands

4479.

Lübke, Marco
Neuartige multifunktionelle Tenside auf Basis nachwachsender Rohstoffe
2021

4478.

Claus, L.; Bolten, Matthias
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4477.

Claus, L.; Bolten, M.
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4476.

Claus, L.; Bolten, M.
Non-overlapping block smoothers for the Stokes equations
Num. Lin. Alg. Appl., 28 (6) :e2389
2021

4475.

Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia
Nonconvex constrained optimization by a filtering branch and bound
Journal of Global Optimization, 80 :31-61
2021

4474.

Mironchenko, Andrii; Kawan, Christoph; Glück, Jochen
Nonlinear small-gain theorems for input-to-state stability of infinite interconnections
Math. Control Signals Systems, 33 (4) :573--615
2021

4473.

Krämer, Veronika; Barwari, Beawer; Burgmann, Sebastian; Rohde, Martin; Rentschler, Simon; Holzknecht, Christopher; Gmelin, Christoph; Janoske, Uwe
Numerical analysis of an adhering droplet applying an adapted feedback deceleration technique
International Journal of Multiphase Flow, 145 :103808
Dezember 2021
Herausgeber: Elsevier {BV}

4472.

Jacob, Birgit; Zwart, Hans
Observability for port-Hamiltonian systems
European Control Conference (ECC) :2052-2057
2021

4471.

Markert, Clara; Thinius, Marco; Lehmann, Laura; Heintz, Chris; Stappert, Florian; Wissdorf, Walter; Kersten, Hendrik; Benter, Thorsten; Schneider, Bradley B.; Covey, Thomas R.
Observation of charged droplets from electrospray ionization (ESI) plumes in API mass spectrometers
Analytical and Bioanalytical Chemistry
Juli 2021
ISSN: 1618-2642, 1618-2650

4470.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3)
2021

4469.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3) :Paper No. e2301, 30
2021

4468.

Friedhoff, S.; Southworth, B. S.
On "optimal" $h$-independent convergence of parareal and multigrid-reduction-in-time using Runge-Kutta time integration
Numer. Linear Algebra Appl., 28 (3) :Paper No. e2301, 30
2021

4467.

Farkas, Bálint; Friesen, Martin; Rüdiger, Barbara; Schroers, Dennis
On a class of stochastic partial differential equations with multiple invariant measures
NoDEA
2021