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
- 2005
1379.
Short, Luke Chandler; Benter, Thorsten
Real-Time Analysis of Exhaled Breath with MPLI-MS: Observed Nitric Oxide Profile
Chest, 128 (4) :236S
20051378.
[german] Tausch, Michael W.; Seesing, Michael
Redoxreaktionen an Nano-Titandioxid
Praxis der Naturwissenschaften - Chemie in der Schule, 54 (3) :16--19
20051377.
Farkas, Bálint; Révész, Szilárd Gy.
Rendezvous numbers in normed spaces
Bull. Austral. Math. Soc., 72 (3) :423-440
20051376.
Yurchenko, Sergey N.; Thiel, Walter; Carvajal, Miguel; Lin, Hai; Jensen, Per
Rotation-Vibration Motion of Pyramidal XY\(_{3}\) Molecules Described in the Eckart Frame: The Calculation of Intensities with Application to NH\(_{3}\)
Advances in Quantum Chemistry, 48 :209-238
2005
Herausgeber: Academic Press1375.
Yurchenko, Sergey N.; Thiel, Walter; Carvajal, Miguel; Lin, Hai; Jensen, Per
Rotation-Vibration Motion of Pyramidal XY\(_{3}\) Molecules Described in the Eckart Frame: The Calculation of Intensities with Application to NH\(_{3}\)
Advances in Quantum Chemistry, 48 :209-238
2005
Herausgeber: Academic Press1374.
Yurchenko, Sergei N.; Carvajal, Miguel; Jensen, Per; Lin, Hai; Zheng, Jingjing; Thiel, Walter
Rotation-vibration motion of pyramidal XY\(_{3}\) molecules described in the Eckart frame: Theory and application to NH\(_{3}\)
Molecular Physics, 103 (2-3) :359-378
20051373.
Yurchenko, Sergei N.; Carvajal, Miguel; Jensen, Per; Lin, Hai; Zheng, Jingjing; Thiel, Walter
Rotation-vibration motion of pyramidal XY\(_{3}\) molecules described in the Eckart frame: Theory and application to NH\(_{3}\)
Molecular Physics, 103 (2-3) :359-378
20051372.
Yurchenko, Sergey N.; Thiel, Walter; Carvajal, Miguel; Lin, Hai; Jensen, Per
Rotation-Vibration Motion of Pyramidal XY3 Molecules Described in the Eckart Frame: The Calculation of Intensities with Application to NH3
Advances in Quantum Chemistry, 48 :209-238
2005
Herausgeber: Academic Press1371.
Yurchenko, Sergei N.; Carvajal, Miguel; Jensen, Per; Lin, Hai; Zheng, Jingjing; Thiel, Walter
Rotation-vibration motion of pyramidal XY3 molecules described in the Eckart frame: Theory and application to NH3
Molecular Physics, 103 (2-3) :359-378
20051370.
Short, Luke Chandler; Benter, Thorsten
Selective measurement of HCHO in urine using direct liquid-phase fluorimetric analysis
Clinical Chemistry and Laboratory Medicine (CCLM), 43 (2) :178-182
2005
Herausgeber: De Gruyter1369.
Short, Luke Chandler; Benter, Thorsten
Selective measurement of HCHO in urine using direct liquid-phase fluorimetric analysis
Clinical Chemistry and Laboratory Medicine (CCLM), 43 (2) :178-182
2005
Herausgeber: De Gruyter1368.
Short, Luke Chandler; Benter, Thorsten
Selective measurement of HCHO in urine using direct liquid-phase fluorimetric analysis
Clinical Chemistry and Laboratory Medicine (CCLM), 43 (2) :178-182
2005
Herausgeber: De Gruyter1367.
[english] Rohe, Bernd; S. Veeman, W.; Tausch, Michael W.
Synthesis and photocatalytic activity of silane-coated and UV-modified nanoscale zinc oxide
Nanotechnology, 17 (1) :277--282
2005
Herausgeber: {IOP} Publishing1366.
Tausch, Michael W.
Teaching Photochemistry with Microscale Experiments. A Contribution for the Ongoing Curriculum Modernisation
Educaci{\'o}n Qu{\'i}mica, 16 (4) :529
2005
Herausgeber: Universidad Nacional Autonoma de Mexico1365.
Yurchenko, Sergey N.; Thiel, Walter; Patchkovskii, Serguei; Jensen, Per
Theoretical evidence for the formation of rotational energy level clusters in the vibrational ground state of PH\(_{3}\)
Physical Chemistry Chemical Physics, 7 (4) :573-582
20051364.
Yurchenko, Sergey N.; Thiel, Walter; Patchkovskii, Serguei; Jensen, Per
Theoretical evidence for the formation of rotational energy level clusters in the vibrational ground state of PH\(_{3}\)
Physical Chemistry Chemical Physics, 7 (4) :573-582
20051363.
Yurchenko, Sergey N.; Thiel, Walter; Patchkovskii, Serguei; Jensen, Per
Theoretical evidence for the formation of rotational energy level clusters in the vibrational ground state of PH3
Physical Chemistry Chemical Physics, 7 (4) :573-582
20051362.
Bohrmann-Linde, Claudia
Umweltschutz durch Elektrochemie: Elektrokoagulation von ''echtem'' Abwasser
Praxis der Naturwissenschaften - Chemie in der Schule, 53 (3)
20051361.
Imhof, David; Weingartner, Ernest; Vogt, Ulrich; Dreiseidler, A.; Rosenbohm, E.; Scheer, Volker; Vogt, Rainer; Nielsen, O. J.; Kurtenbach, Ralf; Corsmeier, Ulrich; Kohler, M.; Baltensperger, Urs
Vertical distribution of aerosol particles and NO\(_{x}\) close to a motorway
Atmospheric Environment, 39 (31) :5710-5721
2005
Herausgeber: Pergamon1360.
Imhof, David; Weingartner, Ernest; Vogt, Ulrich; Dreiseidler, A.; Rosenbohm, E.; Scheer, Volker; Vogt, Rainer; Nielsen, O. J.; Kurtenbach, Ralf; Corsmeier, Ulrich; Kohler, M.; Baltensperger, Urs
Vertical distribution of aerosol particles and NO\(_{x}\) close to a motorway
Atmospheric Environment, 39 (31) :5710-5721
2005
Herausgeber: Pergamon1359.
Imhof, David; Weingartner, Ernest; Vogt, Ulrich; Dreiseidler, A.; Rosenbohm, E.; Scheer, Volker; Vogt, Rainer; Nielsen, O. J.; Kurtenbach, Ralf; Corsmeier, Ulrich; Kohler, M.; Baltensperger, Urs
Vertical distribution of aerosol particles and NOx close to a motorway
Atmospheric Environment, 39 (31) :5710-5721
2005
Herausgeber: Pergamon1358.
Pulch, Roland
Warped MPDAE models including minimisation criteria for the simulation of RF signals
PAMM: Proceedings in Applied Mathematics and Mechanics, 5 (1) :811–814
2005
Herausgeber: WILEY-VCH Verlag1357.
Tausch, Michael W.
Weißpigment und Photokatalysator
Praxis der Naturwissenschaften - Chemie in der Schule, 54 (3) :1
2005- 2004
1356.
Tausch, Michael W.; Seesing, Michael
''Unterricht up-to-date'', Online-Materialien im Rahmen des EU-Projekts ESPERE
Online ( www.espere.net )
20041355.
Al{\`\i}, Giuseppe; Bartel, Andreas
A priori estimates for multiphysics models in electric circuit design
In A. Buikis and R. Ciegis and A. D. Fitt, Editor, Progress in Industrial Mathematics at ECMI 2002, Seite 167--171
Springer Berlin Heidelberg
In A. Buikis and R. Ciegis and A. D. Fitt, Editor
Herausgeber: Springer
2004
