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



2017

3792.

Pinnau, Rene; Totzeck, Claudia; Tse, Oliver; Martin, Stephan
A consensus-based model for global optimization and its mean-field limit
Mathematical Models and Methods in Applied Sciences, 27 (1) :183-204
2017

3791.

Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail; others
A functional limit theorem for irregular SDEs
, Annales de l'Institut Henri Poincaré, Probabilités et StatistiquesBand53, Seite 1438--1457
Institut Henri Poincaré
2017

3790.

Ankirchner, Stefan; Kruse, Thomas; Urusov, Mikhail; others
A functional limit theorem for irregular SDEs
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (3) :1438–1457
2017
Herausgeber: Institute of Mathematical Statistics

3789.

Bolten, Matthias; Moser, D.; Speck, R.
A multigrid perspective on the parallel full approximation scheme in space and time
Numer. Lin. Alg. Appl., 24 (6) :e2110
2017

3788.

Bolten, M.; Moser, D.; Speck, R.
A multigrid perspective on the parallel full approximation scheme in space and time
Numer. Lin. Alg. Appl., 24 (6) :e2110
2017

3787.

Bolten, M.; Moser, D.; Speck, R.
A multigrid perspective on the parallel full approximation scheme in space and time
Numer. Lin. Alg. Appl., 24 (6) :e2110
2017

3786.

Ehrhardt, Matthias
A new two-way artificial boundary condition for wave propagation
23rd AIAA/CEAS Aeroacoustics Conference, Seite 3509
2017

3785.

Ehrhardt, Matthias
A new two-way artificial boundary condition for wave propagation
Seite 3509
2017
3509

3784.

Ehrhardt, Matthias
A new two-way artificial boundary condition for wave propagation
Seite 3509
2017
3509

3783.

Schmiedt, Hanno; Schlemmer, Stephan; Yurchenko, Sergey N.; Yachmenev, Andrey; Jensen, Per
A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules
Physical Chemistry Chemical Physics, 19 (3) :1847-1856
2017
Herausgeber: Royal Society of Chemistry

3782.

Schmiedt, Hanno; Schlemmer, Stephan; Yurchenko, Sergey N.; Yachmenev, Andrey; Jensen, Per
A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules
Physical Chemistry Chemical Physics, 19 (3) :1847-1856
2017
Herausgeber: Royal Society of Chemistry

3781.

Schmiedt, Hanno; Schlemmer, Stephan; Yurchenko, Sergey N.; Yachmenev, Andrey; Jensen, Per
A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules
Physical Chemistry Chemical Physics, 19 (3) :1847-1856
2017
Herausgeber: Royal Society of Chemistry

3780.

Schweitzer, Marcel
A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching
Numer. Algorithms, 76 (1) :1-31
2017

3779.

Schweitzer, Marcel
A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching
Numer. Algorithms, 76 (1) :1-31
2017

3778.

Schweitzer, Marcel
A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching
Numer. Algorithms, 76 (1) :1-31
2017

3777.

Klamroth, Kathrin; Köbis, Elisabeth; Schöbel, Anita; Tammer, Christiane
A unified approach to uncertain optimization
European Journal of Operational Research, 260 :403-420
2017

3776.

Shcherbakov, Dmitry; Ehrhardt, Matthias; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco; Peardon, Michael
Adapted nested force-gradient integrators: The Schwinger model case
Communications in Computational Physics, 21 (4) :1141–1153
2017
Herausgeber: Cambridge University Press

3775.

Shcherbakov, Dmitry; Ehrhardt, Matthias; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco; Peardon, Michael
Adapted nested force-gradient integrators: The Schwinger model case
Communications in Computational Physics, 21 (4) :1141–1153
2017
Herausgeber: Cambridge University Press

3774.

Shcherbakov, Dmitry; Ehrhardt, Matthias; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco; Peardon, Michael
Adapted nested force-gradient integrators: The Schwinger model case
Communications in Computational Physics, 21 (4) :1141–1153
2017
Herausgeber: Cambridge University Press

3773.

Bolten, Matthias; Franchetti, F.; Kelly, P. H.; Lengauer, C.; Mohr, M.
Algebraic description and automatic generation of multigrid methods in SPIRAL
CCPE, 29 (17) :e4105
2017

3772.

Bolten, M.; Franchetti, F.; Kelly, P. H.; Lengauer, C.; Mohr, M.
Algebraic description and automatic generation of multigrid methods in SPIRAL
CCPE, 29 (17) :e4105
2017

3771.

Bolten, M.; Franchetti, F.; Kelly, P. H.; Lengauer, C.; Mohr, M.
Algebraic description and automatic generation of multigrid methods in SPIRAL
CCPE, 29 (17) :e4105
2017

3770.

Ehrhardt, Matthias; Günther, Michael; Pólvora, Pedro
Alternating direction explicit methods for linear, nonlinear and multi-dimensional Black-Scholes models
In Ehrhardt, Matthias and Günther, Michael and ter Maten, E. Jan W., Editor
Seite 333–371
Herausgeber: Springer Cham
2017
333–371

3769.

Ehrhardt, Matthias; Günther, Michael; Pólvora, Pedro
Alternating direction explicit methods for linear, nonlinear and multi-dimensional Black-Scholes models
Novel Methods in Computational Finance :333--371
2017
Herausgeber: Springer International Publishing

3768.

Ehrhardt, Matthias; Günther, Michael; Pólvora, Pedro
Alternating direction explicit methods for linear, nonlinear and multi-dimensional Black-Scholes models
In Ehrhardt, Matthias and Günther, Michael and ter Maten, E. Jan W., Editor
Seite 333–371
Herausgeber: Springer Cham
2017
333–371