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Introduction to Ordinary Differential Equations

Descrizione

Ordinary Differential Equations (ODEs) are the most mathematical tool for modelling and quantifying time dependent processes. Chemical reactions, population growth, mechanical systems are examples for this. Newton's second law is in fact an ODE. In this course, we give an introduction into the basic concepts underlying ODEs from a modeling point of view as well as from a mathematical point of view. We then consider numerical methods for the numerical solution of ODEs and investigate properties such as approximation error and stability. This will include Runge-Kutta Methods and so called BDF methods. We will also shortly investigate modern approaches such as parallel-in-time integration. Numerical examples, programming, and mathematical analysis will be the tools for getting towards an understanding of dynamical systems and their properties.

 

REFERENCES

  • Iserles, Arieh. A first course in the numerical analysis of differential equations. No. 44. Cambridge university press, 2009
  • Deuflhard, Peter, and Folkmar Bornemann. Scientific computing with ordinary differential equations. Vol. 42. Springer Science & Business Media, 2012.
  • E. Hairer, S. P. Nørsett, and G. Wanner. Solving ordinary differential equations. I, volume 8 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 1993. Nonstiff problems
  • E. Hairer and G. Wanner. Solving ordinary differential equations. II, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 1996. Stiff and differential-algebraic problems.

Persone

 

Krause R.

Docente titolare del corso

Pezzuto S.

Docente titolare del corso

Rovi G.

Assistente

Informazioni aggiuntive

Semestre
Autunnale
Anno accademico
2019-2020
ECTS
3
Offerta formativa
Master of Science in Artificial Intelligence, Corso a scelta, Corso, 1° anno

Master of Science in Artificial Intelligence, Corso a scelta, Corso, 2° anno

Master of Science in Computational Science, Corso di base, Corso, 1° anno

Dottorato in Scienze informatiche, Corso a scelta, Corso, 2° anno (2 ECTS)

Dottorato in Scienze informatiche, Corso a scelta, Corso, 1° anno (2 ECTS)