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

4466.

Glück, Jochen
On disjointness, bands and projections in partially ordered vector spaces
Positivity and its applications aus Trends Math.
Seite 141--171
Herausgeber: Birkhäuser/Springer, Cham
2021
141--171

4465.

Glück, Jochen
On the decoupled Markov group conjecture
Bull. Lond. Math. Soc., 53 (1) :240--247
2021

4464.

Farkas, Bálint; Nagy, Béla; Révész, Szilárd Gy.
On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton
2021

4463.

Csomós, Petra; Ehrhardt, Matthias; Farkas, Bálint
Operator splitting for abstract Cauchy problems with dynamical boundary condition
Operators and Matrices, 15 (3) :903–935
2021
Herausgeber: Element d.o.o

4462.

Csomós, Petra; Ehrhardt, Matthias; Farkas, Bálint
Operator splitting for abstract Cauchy problems with dynamical boundary condition
Operators and Matrices, 15 (3) :903–935
2021
Herausgeber: Element d.o.o

4461.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Optimal trade execution in an order book model with stochastic liquidity parameters
SIAM Journal on Financial Mathematics, 12 (2) :788--822
2021
Herausgeber: Society for Industrial and Applied Mathematics

4460.

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Optimal trade execution in an order book model with stochastic liquidity parameters
SIAM Journal on Financial Mathematics, 12 (2) :788–822
2021
Herausgeber: Society for Industrial and Applied Mathematics

4459.

De Sterck, H.; Falgout, R. D.; Friedhoff, S.; Krzysik, O. A.; MacLachlan, S. P.
Optimizing multigrid reduction-in-time and parareal coarse-grid operators for linear advection
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2367, 22
2021

4458.

De Sterck, H.; Falgout, R. D.; Friedhoff, S.; Krzysik, O. A.; MacLachlan, S. P.
Optimizing multigrid reduction-in-time and parareal coarse-grid operators for linear advection
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2367, 22
2021

4457.

De Sterck, H.; Falgout, R. D.; Friedhoff, S.; Krzysik, O. A.; MacLachlan, S. P.
Optimizing multigrid reduction-in-time and parareal coarse-grid operators for linear advection
Numer. Linear Algebra Appl., 28 (4) :Paper No. e2367, 22
2021

4456.

Aragão Belé, Tiago Gomes; Neves, Tauany F.; Cristale, Joyce; Prediher, Patrícia; Constapel, Marc; Dantas, Renato F.
Oxidation of microplastics by O3 and O3/H2O2: Surface modification and adsorption capacity
Journal of Water Process Engineering, 41
2021

4455.

Goettlich, Simone; Totzeck, Claudia
Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks
Mathematics of Control, Signals, and Systems, 34 :185-214
2021

4454.

Kulchytska-Ruchka, I.; Schöps, S.; Hinze, M.; Friedhoff, S.; Ulbrich, S.
PASIROM: parallel simulation and robust optimization of electro-mechanical energy converters
, German success stories in industrial mathematics Band 35 aus Math. Ind.
Seite 135-140
Herausgeber: Springer, Cham
2021
135-140

4453.

Kulchytska-Ruchka, I.; Schöps, S.; Hinze, M.; Friedhoff, S.; Ulbrich, S.
PASIROM: parallel simulation and robust optimization of electro-mechanical energy converters
, German success stories in industrial mathematics Band 35 aus Math. Ind.
Seite 135-140
Herausgeber: Springer, Cham
2021
135-140

4452.

Kulchytska-Ruchka, I.; Schöps, S.; Hinze, M.; Friedhoff, S.; Ulbrich, S.
PASIROM: parallel simulation and robust optimization of electro-mechanical energy converters
, German success stories in industrial mathematics Band 35 aus Math. Ind.
Seite 135-140
Herausgeber: Springer, Cham
2021
135-140

4451.

[english] Zimmermann, Marc; Domke, Dennis; Schween, Michael
Photobromination (SR) and Corresp. SN1 Reactions – Key Reactions for the Development and the Application of the Concept of Hyperconjugation
World Journal of Chemical Education, 9 :175-184
2021

4450.

Ehrhardt, Matthias
Pricing basket default swaps using quasi-analytic techniques
Decisions in Economics and Finance, 44 :241–267
2021
Herausgeber: Springer Verlag Italia

4449.

Ehrhardt, Matthias
Pricing basket default swaps using quasi-analytic techniques
Decisions in Economics and Finance, 44 :241–267
2021
Herausgeber: Springer Verlag Italia

4448.

Ehrhardt, Matthias
Pricing basket default swaps using quasi-analytic techniques
Decisions in Economics and Finance, 44 :241--267
2021
Herausgeber: Springer International Publishing

4447.

Stiglmayr, Michael; Gaul, Daniela
Projekt Ride-Hailing Wuppertal
In Matthias Ehrhardt and Michael G, Editor, Erfolgsformeln - Anwendungen der Mathematik
2021

4446.

Frommer, Andreas; Jacob, Birgit; Vorberg, Lukas; Wyss, Christian; Zwaan, Ian
Pseudospectrum enclosures by discretization
Integral Equations OperatorTheory, 93 :Article No 9, 32 p.
2021

4445.

Celik, Ibrahim E.
Reactivity of Organic Geminal Diazides at Tetrahedral Carbons
European Journal of Organic Chemistry, 2021 (1) :53–63
2021
ISSN: 1434-193X, 1099-0690

4444.

Bannenberg, MWFM; Ciccazzo, A
Reduced order multirate schemes for coupled differential-algebraic systems
Applied Numerical Mathematics, 168 :104--114
2021
Herausgeber: North-Holland

4443.

Bannenberg, MWFM; Ciccazzo, A
Reduced order multirate schemes for coupled differential-algebraic systems
Applied Numerical Mathematics, 168 :104–114
2021
Herausgeber: North-Holland

4442.

Bannenberg, MWFM; Ciccazzo, A
Reduced order multirate schemes for coupled differential-algebraic systems
Applied Numerical Mathematics, 168 :104–114
2021
Herausgeber: North-Holland