Università Roma Tre

Ordinary Differential Equations
Finite difference methods for Ordinary Differential Equations: Euler method. Consistency, stability, absolute stability. Second-order Runge-Kutta methods. Implicit one-step methods: backward Euler, Crank-Nicolson. Convergence of one-step methods.
Multistep methods: general structure, complexity, absolute stability. Stability and consistency for multistep methods. Adams methods. BDF methods. Predictor-Corrector methods. (reference: chapter 7 of the notes "Appunti del corso di Analisi Numerica")

Difference schemes for Partial Differential Equations
General concepts about finite difference approximations. Semi-discrete approximations and their convergence. Lax-Richtmeyer theorem.
The advection equation: method of characteristics. Semi-dicrete and fully discrete upwind method, consistency and stability. The heat equation: Fourier approximation. Centred finite difference approximation, consistency and stability. Poisson equation: Fourier and centred difference approximations, convergence study. (Reference: notes by R. LeVeque, "Finite Difference methods for differential equations", selected material from chapters 1, 2, 3, 12, 13)

N.B.: References are provided with respect to the course notes.

Roberto Ferretti, "Appunti del corso di Analisi Numerica", available at the address: http://www.mat.uniroma3.it/users/ferretti/corso.pdf

Roberto Ferretti, "Esercizi d'esame di Analisi Numerica", available at the address: http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf

Slides of the lessons, available from the course page: http://www.mat.uniroma3.it/users/ferretti/bacheca.html

Additional notes provided by the teacher