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



2022

4816.

[english] Mertineit, Ann-Kathrin; Burdinski, Dirk; Zulauf, Bert; Hackradt, Hans; Meuter, Nico; Bohrmann-Linde, Claudia; Schaper, Klaus
Helping Digital Natives to Become Digital Natives Through Production Standards, Research AND Quality Ssystems?
Seite 3913-3920
2022

ISBN: 978-84-09-45476-1

4815.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher Strong Order Methods for linear {Itô} {SDEs} on matrix {Lie} Groups
BIT Numer. Math.
Januar 2022
Herausgeber: Springer
ISSN: 1572-9125

4814.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear It{\^o} SDEs on matrix Lie groups
BIT Numerical Mathematics :1--25
2022
Herausgeber: Springer Netherlands Dordrecht

4813.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear Itô SDEs on matrix Lie groups
BIT Numerical Mathematics, 62 (3) :1095–1119
2022
Herausgeber: Springer Netherlands

4812.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear Itô SDEs on matrix Lie groups
BIT Numerical Mathematics, 62 (3) :1095–1119
2022
Herausgeber: Springer Netherlands

4811.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear Itô SDEs on matrix Lie groups
BIT Numerical Mathematics, 62 (3) :1095–1119
2022
Herausgeber: Springer Netherlands

4810.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear Itô SDEs on matrix Lie groups
BIT Numerical Mathematics :1--25
2022
Herausgeber: Springer Netherlands Dordrecht

4809.

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Higher strong order methods for linear Ito SDEs on matrix Lie groups (Jan, 10.1007/s10543-021-00905-9, 2022)
BIT Numerical Mathematics, 62 (3) :1093--1093
2022
Herausgeber: SPRINGER VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS

4808.

Nowaczyk, Nikolai; Kienitz, Jörg; Acar, Sarp Kaya; Liang, Qian
How deep is your model? Network topology selection from a model validation perspective
Journal of Mathematics in Industry, 12 (1) :1
2022
Herausgeber: Springer Verlag

4807.

Nowaczyk, N.; Kienitz, J.; Acar, S. K.; Liang, Q.
How deep is your model? Network topology selection from a model validation perspective
JMI, 12 (1)
2022

4806.


Hypervalent Iodine-Mediated Azidation Reactions
European Journal of Organic Chemistry (34)
2022
ISSN: 1434-193X

4805.

Henkel, Marvin-Lucas; Kasolis, Fotios; Clemens, Markus; Günther, Michael; Schöps, Sebastian
Implicit Gauging of Electromagneto-Quasistatic Field Formulations
IEEE Transactions on Magnetics, 58 (9) :1--4
2022
Herausgeber: IEEE

4804.

Henkel, Marvin-Lucas; Kasolis, Fotios; Clemens, Markus; Günther, Michael; Schöps, Sebastian
Implicit gauging of electromagneto-quasistatic field formulations
IEEE Transactions on Magnetics, 58 (9) :1–4
2022
Herausgeber: IEEE

4803.

Henkel, Marvin-Lucas; Kasolis, Fotios; Clemens, Markus; Günther, Michael; Schöps, Sebastian
Implicit gauging of electromagneto-quasistatic field formulations
IEEE Transactions on Magnetics, 58 (9) :1–4
2022
Herausgeber: IEEE

4802.

Ackermann, Julia; Kruse, Thomas; Overbeck, Ludger
Inhomogeneous affine Volterra processes
Stochastic Processes and their Applications, 150 :250–279
2022
Herausgeber: North-Holland

4801.

Ackermann, Julia; Kruse, Thomas; Overbeck, Ludger
Inhomogeneous affine Volterra processes
Stochastic Processes and their Applications, 150 :250--279
2022
Herausgeber: North-Holland

4800.

Ackermann, Julia; Kruse, Thomas; Overbeck, Ludger
Inhomogeneous affine Volterra processes
Stochastic Processes and their Applications, 150 :250–279
2022
Herausgeber: North-Holland

4799.

Burgmann, Sebastian; Krämer, Veronika; Rohde, Martin; Dues, Michael; Janoske, Uwe
Inner and outer flow of an adhering droplet in shear flow
International Journal of Multiphase Flow, 153 :104140
2022
ISSN: 0301-9322

4798.

Hosfeld, René; Jacob, Birgit; Schwenninger, Felix
Integral input-to-state stability of unbounded bilinear control systems
Math. Control Signals Systems, 34 (2) :273-295
2022

4797.

Schweitzer, Marcel
Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
2022

4796.

Tovar, Carmen Maria; Barnes, Ian; Bejan, Iustinian Gabriel; Wiesen, Peter
Kinetic study of the atmospheric oxidation of a series of epoxy compounds by OH radicals
Atmospheric Chemistry and Physics, 22 (10) :6989—7004
Mai 2022
ISSN: 1680-7324

4795.

Cardona, Alejandro L.; Gibilisco, Rodrigo G.; Rivela, Cynthia B.; Blanco, María B.; Patroescu-Klotz, Iulia; Illmann, Niklas; Wiesen, Peter; Teruel, Mariano A.
Kinetics, product distribution and atmospheric implications of the gas-phase oxidation of allyl sulfides by OH radicals
Chemosphere, 288 :132546
Februar 2022
ISSN: 00456535

4794.

Bolten, Matthias; Sturler, E. De; Hahn, C.
Krylov Subspace Recycling for Evolving Structures
Comput. Methods Appl. Mech. Engrg., 391 :114222
2022

4793.

Bolten, M.; Sturler, E. De; Hahn, C.
Krylov Subspace Recycling for Evolving Structures
Comput. Methods Appl. Mech. Engrg., 391 :114222
2022

4792.

Bolten, M.; De Sturler, E.; Hahn, C.
Krylov Subspace Recycling for Evolving Structures
Comput. Methods Appl. Mech. Engrg., 391 :114222
2022