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
- scheduled 2023
6180.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer
scheduled 20236179.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer6178.
Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific6177.
Teng, Long; Ehrhardt, Matthias; G\"unther, Michael
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific
scheduled 20236176.
{Duffy, D.; Kienitz, J.}
Monte Carlo Frameworks - Building Customisable and High-performance C++ Applications
Herausgeber: {John Wiley \& Sons, Chichester}6175.
{Kienitz, J.}
Stochastic Processes in Finance I
{Wilmott Magazine}6174.
{Kienitz, J.}
Stochastic Processes in Finance II
{Wilmott Magazine}, {6}6173.
{Kienitz, J.}
Stochastic Processes in Finance III
{Wilmott Magazine}- {2009}
6172.
{Beyer, P.; Kienitz, J.}
{Pricing {F}orward {S}tart {O}ption in {M}odels based on {L}évy {P}rocesses}
{The Icfai University Journal of Derivatives Markets}, {6(2)} :{7--23}
{2009}6171.
{Kienitz, J.}
{The {CGMY} model}
{The Encyclopedia of Quantitative Finance (ed. Cont), Wiley}
{2009}6170.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer6169.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer6168.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer6167.
Ehrhardt, M.; Günther, M.
Numerik gewöhnlicher Differentialgleichungen : Anwendungen in Technik, Wirtschaft, Biologie und Gesellschaft
Herausgeber: Springer- 2023
6166.
Jacob, Birgit; Totzeck, Claudia
Port-Hamiltonian structure of interacting particle systems and its mean-field limit
20236165.
Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch \& Bound with Scalarization-Based Information
Submitted to Mathematical Methods of Operations Research
2023
Herausgeber: arXiv6164.
Carrillo, Jose Antonio; Totzeck, Claudia; Vaes, Urbain
Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints
, Modeling and Simulation for Collective Dynamics,Lecture Notes Series, Institute for Mathematical Sciences, NUS Band 40
20236163.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Kompetenzförderung durch Erklärvideos in einem Selbstlernbuch zum Einstieg in die Organische Chemie
MNU-Journal, 01.2023 :48-54
2023
ISSN: 0025-58666162.
Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific6161.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Mit Lactase und Lactose zum elektrischen Strom - enzymatische Brennstoffzellen auf Filterpapierbasis für den Chemieunterricht.
CHEMKON, 30 (1) :37-41
Januar 20236160.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
20236159.
[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 20236158.
Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific6157.
Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific6156.
Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific