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

2000

917.

Tyuterev, Vladimir G.; Cours, T.; Tashkun, Sergey A.; Barbe, Alain; Jensen, Per
Potential function of the ozone molecule: global calculations of the rovibrational states and the dissociation behavior
In Sinitsa, Leonid N., Editor, 13th Symposium and School on High-Resolution Molecular SpectroscopyBand4063, Seite 142
In Sinitsa, Leonid N., Editor
Herausgeber: International Society for Optics and Photonics
2000

DOI: 10.1117/12.375367

916.

Günther, Michael; Simeon, Bernd
Praktikum Wissenschaftliches Rechnen auf dem HRZ-Vektorparallelrechner VPP
2000

915.

Denk, Ceorg; Günther, Michael; Kahlert, Martin; Paffrath, Meinhard; Rentrop, Peter; Wever, Utz; Zheng, Q
Recent advances in electronic industry by numerical simulation
2000

914.

Günther, Michael
Semidiscretization may act like a deregularization
Mathematics and Computers in Simulation, 53 (4) :293–301
2000
Herausgeber: Elsevier

DOI: 10.1016/S0378-4754(00)00216-0

913.

Günther, Michael
Semidiscretization may act like a deregularization
Mathematics and computers in simulation, 53 (4-6) :293--301
2000
Herausgeber: North-Holland

912.

Kleffmann, Jörg; Becker, Karl Heinz; Br{ö}ske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O and HNO\(_{3}\)/H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000

DOI: 10.1021/jp000815u

911.

Kleffmann, Jörg; Becker, Karl Heinz; Br{ö}ske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O and HNO\(_{3}\)/H\(_{2}\)SO\(_{4}\)/H\(_{2}\)O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000

DOI: 10.1021/jp000815u

910.

Kleffmann, Jörg; Becker, Karl Heinz; Bröske, Rolf; Rothe, Dieter; Wiesen, Peter
Solubility of HBr in H2SO4/H2O and HNO3/H2SO4/H2O Solutions
The Journal of Physical Chemistry A, 104 (37) :8489-8495
2000

DOI: 10.1021/jp000815u

909.

Tausch, Michael W.
Stoffkreisläufe
Praxis der Naturwissenschaften - Chemie in der Schule, 49 (7) :1
2000

908.

Bludsk{{\'y}}, Ota; Nachtigall, Petr; Hrus{{\'a}}k, Jan; Jensen, Per
The calculation of the vibrational states of SO\(_{2}\) in the C\verb=~= \(^{1}\)B\(_{2}\) electronic state up to the SO(\(^{3}\)\(\Sigma\)\(^{-}\))+O(\(^{3}\)P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000

DOI: 10.1016/S0009-2614(00)00015-4

907.

Bludsk{{\'y}}, Ota; Nachtigall, Petr; Hrus{{\'a}}k, Jan; Jensen, Per
The calculation of the vibrational states of SO\(_{2}\) in the C\verb=~= \(^{1}\)B\(_{2}\) electronic state up to the SO(\(^{3}\)\(\Sigma\)\(^{-}\))+O(\(^{3}\)P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000

DOI: 10.1016/S0009-2614(00)00015-4

906.

Bludský, Ota; Nachtigall, Petr; Hrusák, Jan; Jensen, Per
The calculation of the vibrational states of SO2 in the C~ 1B2 electronic state up to the SO(3Σ-)+O(3P) dissociation limit
Chemical Physics Letters, 318 (6) :607-613
2000

DOI: 10.1016/S0009-2614(00)00015-4

905.

Denk, Georg; Günther, Michael
The influence of MOSFET model and network equations on circuit simulation
2000

904.

Klamroth, Kathrin; Wiecek, Margaret M.
Time-dependent capital budgeting with multiple criteria
In Haimes, Y.Y. and Steuer, R.E., Editor, Research and Practice in Multiple Criteria Decision MakingBand487ausLecture Notes in Economics and Mathematical Systems, Seite 421-432
In Haimes, Y.Y. and Steuer, R.E., Editor
Herausgeber: Springer-Verlag
2000

DOI: 10.1007/978-3-642-57311-8_36

903.

East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; D{é}ch{{\`e}}ne, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S\(_{1}\)-S\(_{0}\) fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000

DOI: 10.1063/1.480571

902.

East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; D{é}ch{{\`e}}ne, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S\(_{1}\)-S\(_{0}\) fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000

DOI: 10.1063/1.480571

901.

East, Allan L.L.; Liu, Haisheng; Lim, Edward C.; Jensen, Per; Déchène, Isabelle; Zgierski, Marek Z.; Siebrand, Willem; Bunker, Philip R.
Toluene internal-rotation: Measurement and simulation of the high-resolution S1-S0 fluorescence excitation spectrum at 0.5 K
Journal of Chemical Physics, 112 (1) :167-175
2000

DOI: 10.1063/1.480571

900.

Denk, Georg; Feldmann, Uwe; Günther, Michael; Rentrop, Peter
Topics in Electric Circuit Simulation
2000

899.

Tausch, Michael W.; Schmitz, R.-P.
Tropfsteinhöhlen und Kreislauf des Kohlenstoffdioxids in der Natur - eine Anwendung für Internet und CD-ROM
Praxis der Naturwissenschaften - Chemie in der Schule, 49 (7) :13
2000

898.

Schandl, Bernd; Klamroth, Kathrin; Wiecek, Margaret M.
Using block norms in bicriteria optimization
In Haimes, Y.Y. and Steuer, R.E., Editor, Research and Practice in Multiple Criteria Decision MakingBand487ausLecture Notes in Economics and Mathematical Systems, Seite 149-160
In Haimes, Y.Y. and Steuer, R.E., Editor
Herausgeber: Springer-Verlag
2000

DOI: 10.1007/978-3-642-57311-8_12

897.

Brust, A. S.; Becker, Karl Heinz; Kleffmann, Jörg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon

DOI: 10.1016/S1352-2310(99)00322-2

896.

Brust, A. S.; Becker, Karl Heinz; Kleffmann, Jörg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon

DOI: 10.1016/S1352-2310(99)00322-2

895.

Brust, A. S.; Becker, Karl Heinz; Kleffmann, Jörg; Wiesen, Peter
UV absorption cross sections of nitrous acid
Atmospheric Environment, 34 (1) :13-19
2000
Herausgeber: Pergamon

DOI: 10.1016/S1352-2310(99)00322-2

894.

Tyuterev, Vladimir G.; Tashkun, Sergey A.; Schwenke, D. W.; Jensen, Per; Cours, T.; Barbe, Alain; Jacon, M.
Variational EKE-calculations of rovibrational energies of the ozone molecule from an empirical potential function
Chemical Physics Letters, 316 (3-4) :271-279
2000

DOI: 10.1016/S0009-2614(99)01228-2

893.

Tyuterev, Vladimir G.; Tashkun, Sergey A.; Schwenke, D. W.; Jensen, Per; Cours, T.; Barbe, Alain; Jacon, M.
Variational EKE-calculations of rovibrational energies of the ozone molecule from an empirical potential function
Chemical Physics Letters, 316 (3-4) :271-279
2000

DOI: 10.1016/S0009-2614(99)01228-2