Nonlinear ordinary differential equations: perturbation methods & applications - Dottorato in TECNOLOGIE DELL'INFORMAZIONE E DELLE COMUNICAZIONI (ICT) (A.A. 2021-2022)
Master Course Seminars A.A. 2021/22 (4 hours):
tools to solve nonlinear problems
Instructor: Sandra Carillo
Dipartimento di Scienze di Base e Applicate per l’Ingegneria
Sapienza Universit`a di Roma Sandra.Carillo@sbai.uniroma1.it http://www.sbai.uniroma1.it/~sandra.carillo
Seminars Description: The aim of these Seminars is to provide some ideas on methods to study
nonlinear problems modelled via nonlinear ordinary differential equations. Specifically, a brief
overview on ad hoc methods developed when a small parameter appears is given. T
he examples of weakly damped oscillator (toy problem) and the physical pendulum are considered
to illustrate the methods.
Monday March 21, 17.30 -19.30
Monday March 28, 17.30 -19.30
The arguments can be schematically listed in:
- Qualitative methods: an introduction.
- Straightforward Perturbation Method.
- Multiple Scale Method.
The results are visualised via computer algebra manipulation (MATLAB’ Tollbox).
Texts: Selected Chapters from
M.H.Holmes, Introduction to Perturbation Methods, M.H.Holmes, Introduction to Pertur- bation Methods, Springer, New York, 1995; Author(s): M.H.Holmes; ISBN-13: 978- 0000000000
M. Lo Schiavo, Note di sistemi dinamici, SIMAI e-Lecture Notes, Vol 12 (2013) http://cab.unime.it/journals/index.php/lecture/article/view/928, ISBN-13:978- 88-905708-5-8
Further material is provided by the Instructor.