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

2005

1387.

George, Christian; Strekowski, R. S.; Kleffmann, J{ö}rg; Stemmler, Konrad; Ammann, Markus
Photoenhanced uptake of gaseous NO\(_{2}\) on solid organic compounds: a photochemical source of HONO?
Faraday Discussions, 130 :195
2005
Herausgeber: The Royal Society of Chemistry

DOI: 10.1039/b417888m

1386.

George, Christian; Strekowski, R. S.; Kleffmann, J{ö}rg; Stemmler, Konrad; Ammann, Markus
Photoenhanced uptake of gaseous NO\(_{2}\) on solid organic compounds: a photochemical source of HONO?
Faraday Discussions, 130 :195
2005
Herausgeber: The Royal Society of Chemistry

DOI: 10.1039/b417888m

1385.

George, Christian; Strekowski, R. S.; Kleffmann, Jörg; Stemmler, Konrad; Ammann, Markus
Photoenhanced uptake of gaseous NO2 on solid organic compounds: a photochemical source of HONO?
Faraday Discussions, 130 :195
2005
Herausgeber: The Royal Society of Chemistry

DOI: 10.1039/b417888m

1384.

[german] Tausch, Michael W.; Seesing, Michael; G. Ibanez, J.; Mena-Brito, R.; Fregoso-Infante, A.
Photoredoxreaktionen mit Nano-Titandioxid
Praxis der Naturwissenschaften - Chemie in der Schule, 54 (3) :22--24
2005

1383.

Dearing, P.M.; Klamroth, Kathrin; Segars, R. Jr.
Planar location problems with block distance and barriers
Annals of Operations Research, 136 :117-143
2005

DOI: 10.1007/s10479-005-2042-4

1382.

Es-Sarhir, Abdelhadi; Farkas, Bálint
Positivity of perturbed Ornstein-Uhlenbeck semigroups on C\sb b(H)
Semigroup Forum, 70 (2) :208--224
2005

DOI: 10.1007/s00233-004-0167-4

1381.

Yurchenko, Sergei N.; Zheng, Jingjing; Lin, Hai; Jensen, Per; Thiel, Walter
Potential-energy surface for the electronic ground state of NH\(_{3}\) up to 20000 cm\(^{-1}\) above equilibrium
The Journal of Chemical Physics, 123 (13) :134308
2005

DOI: 10.1063/1.2047572

1380.

Yurchenko, Sergei N.; Zheng, Jingjing; Lin, Hai; Jensen, Per; Thiel, Walter
Potential-energy surface for the electronic ground state of NH\(_{3}\) up to 20000 cm\(^{-1}\) above equilibrium
The Journal of Chemical Physics, 123 (13) :134308
2005

DOI: 10.1063/1.2047572

1379.

Yurchenko, Sergei N.; Zheng, Jingjing; Lin, Hai; Jensen, Per; Thiel, Walter
Potential-energy surface for the electronic ground state of NH3 up to 20000 cm-1 above equilibrium
The Journal of Chemical Physics, 123 (13) :134308
2005

DOI: 10.1063/1.2047572

1378.

Vogt, Ulrich; Dreiseidler, A.; Baumbach, G{ü}nter; Kurtenbach, Ralf; Petrea, Monica; Kohler, M.; Corsmeier, Ulrich
Quality assurance of air pollutant measurements during the BAB II field experiment
Atmospheric Environment, 39 (31) :5642-5664
2005
Herausgeber: Pergamon

DOI: 10.1016/j.atmosenv.2005.03.003

1377.

Vogt, Ulrich; Dreiseidler, A.; Baumbach, Günter; Kurtenbach, Ralf; Petrea, Monica; Kohler, M.; Corsmeier, Ulrich
Quality assurance of air pollutant measurements during the BAB II field experiment
Atmospheric Environment, 39 (31) :5642-5664
2005
Herausgeber: Pergamon

DOI: 10.1016/j.atmosenv.2005.03.003

1376.

Vogt, Ulrich; Dreiseidler, A.; Baumbach, G{ü}nter; Kurtenbach, Ralf; Petrea, Monica; Kohler, M.; Corsmeier, Ulrich
Quality assurance of air pollutant measurements during the BAB II field experiment
Atmospheric Environment, 39 (31) :5642-5664
2005
Herausgeber: Pergamon

DOI: 10.1016/j.atmosenv.2005.03.003

1375.

Short, Luke Chandler; Benter, Thorsten
Real-Time Analysis of Exhaled Breath with MPLI-MS: Observed Nitric Oxide Profile
Chest, 128 (4) :236S
2005

DOI: 10.1016/S0012-3692(16)50706-5

1374.

Short, Luke Chandler; Benter, Thorsten
Real-Time Analysis of Exhaled Breath with MPLI-MS: Observed Nitric Oxide Profile
Chest, 128 (4) :236S
2005

DOI: 10.1016/S0012-3692(16)50706-5

1373.

Short, Luke Chandler; Benter, Thorsten
Real-Time Analysis of Exhaled Breath with MPLI-MS: Observed Nitric Oxide Profile
Chest, 128 (4) :236S
2005

DOI: 10.1016/S0012-3692(16)50706-5

1372.

[german] Tausch, Michael W.; Seesing, Michael
Redoxreaktionen an Nano-Titandioxid
Praxis der Naturwissenschaften - Chemie in der Schule, 54 (3) :16--19
2005

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1371.

Farkas, Bálint; Révész, Szilárd Gy.
Rendezvous numbers in normed spaces
Bull. Austral. Math. Soc., 72 (3) :423-440
2005

1370.

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 Press

DOI: 10.1016/S0065-3276(05)48014-4

1369.

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 Press

DOI: 10.1016/S0065-3276(05)48014-4

1368.

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
2005

DOI: 10.1080/002689705412331517255

1367.

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
2005

DOI: 10.1080/002689705412331517255

1366.

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 Press

DOI: 10.1016/S0065-3276(05)48014-4

1365.

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
2005

DOI: 10.1080/002689705412331517255

1364.

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 Gruyter

DOI: 10.1515/CCLM.2005.030

1363.

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 Gruyter

DOI: 10.1515/CCLM.2005.030