Scheda programma d'esame
METODI NUMERICI PER EQUAZIONI DIFFERENZIALI ORDINARIE
|METODI NUMERICI PER EQUAZIONI DIFFERENZIALI ORDINARIE||MAT/08||LEZIONI||48|
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KnowledgeThe students who successfully complete the course will be aware of the main numerical methods for solving ordinary differential equations and will have the ability to apply them in various contexts. Furthermore, they will have acquired the skill to treat real-life problems modeled by differential equations by selecting the algorithms best suited for dealing with them. At the same time, the course is meant to make students well acquainted with the use of specific mathematical software (Matlab or an open-source software equivalent to it); moreover, they will have the ability to develop, as necessary, their own practical implementation of some simple algorithms. The students will be able to reflect critically and creatively on the results of the numerical simulations carried out by them.
Assessment criteria of knowledgeThe student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology.
- Final oral exam
Delivery: face to face
- attending lectures
- individual study
- Laboratory work
SyllabusThe course is divided in two parts, one of which is devoted principally to numerical methods for solving initial value problems (IVPs), and the other, to those for treating boundary value problems (BVPs). IVPs: - One-step methods (Runge-Kutta); multistep methods (Adams' family and BDF); - Convergence properties; - Concept of stability; - Stiff problems. BVPs: - Shooting methods; finite difference methods; Boundary Value Methods.
BibliographyRecommended readings: R. Mattheij, J. Molenaar. Ordinary Differential Equations in Theory and Practice, SIAM 2002. U.M. Ascher, L.R. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM 1998. L. Brugnano, D. Trigiante. Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon and Breach Science Publisher, Amsterdam, 1998. Further bibliography will be indicated.
Work placementA computer room activity is scheduled for the numerical simulation of some properties of the numerical methods presented in the lectures.
Ultimo aggiornamento 14/11/2016 17:27