Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (Extended Abstract) (Invited Talk)

Vladimir P. Gerdt, Wolfram Koepf, E. W. Mayr und E. V. Vorozhtsov (Editoren)
Andreas Weber, Thomas Sturm, W. M. Seiler und Essam O. Abdel-Rahman
In proceedings of Computer Algebra in Scientific Computing - 12th International Workshop (CASC 2010), Tsakhkadzor, Armenia, pages 267-279, Springer, Sept. 2010
 

Abstract

Investigating oscillations for parametric ordinary differential equations (ODEs) has many applications in science and engineering but is a very hard problem.

We review some recently developed criteria which give sufficient conditions to exclude oscillations by reducing them to problems on semi-algebraic sets—for polynomial vector fields. We will give some examples and we will discuss possible future work in the form of problems to be solved. Some of these problems might be rather immediate to be solved, some others might pose major challenges.

Bibtex

@INPROCEEDINGS{WeberSturmSeilerAbdelRahman2010a,
     author = {Weber, Andreas and Sturm, Thomas and Seiler, W. M. and Abdel-Rahman, Essam O.},
     editor = {Gerdt, Vladimir P. and Koepf, Wolfram and Mayr, E. W. and Vorozhtsov, E. V.},
      pages = {267--279},
      title = {Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for
               Excluding Oscillations (Extended Abstract) (Invited Talk)},
  booktitle = {Computer Algebra in Scientific Computing - 12th International Workshop (CASC 2010)},
     series = {Lecture Notes in Computer Science},
     volume = {6244},
       year = {2010},
      month = sep,
  publisher = {Springer},
   location = {Tsakhkadzor, Armenia},
   abstract = {Investigating oscillations for parametric ordinary differential equations (ODEs) has many
               applications in science and engineering but is a very hard problem.
               
               We review some recently developed criteria which give sufficient conditions to exclude oscillations
               by reducing them to problems on semi-algebraic sets---for polynomial vector fields. We will give
               some examples and we will discuss possible future work in the form of problems to be solved. Some of
               these problems might be rather immediate to be solved, some others might pose major challenges.},
        doi = {10.1007/978-3-642-15274-0_24}
}