Università degli Studi di Roma "Tor Vergata"

Synthetic program
Part I. [1]
Introduction to finite differences and finite elements.
Methods for partial differential equations in zero dimensions: the BVP of ordinary differential equations.
Finite difference methods for elliptic equations

Part II [1]
Initial value problems for partial differential equations in zero spatial dimensions, the IVPs of ODEs
Zero-Stability and convergence for initial value problems
A-and L- stability and methods for stiff problems

Part III [1]
Classification of linear partial differential equations of second order elliptic, parabolic, hyperbolic
Derivation of the PDE conservation laws and transport, diffusion, reaction-diffusion, transport-diffusion, transport-reaction-diffusion
Fourier analysis of linear PDEs
Diffusion equation
Transport equation and outline methods for hyperbolic systems
Methods of high order
Nonlinear conservation laws

Part IV. [2]
Solution linear systems large and sparse generated from time to time by discrete and semidiscrete models. Notes on the efficient solution of some linear structured systems.

Part V. [*]
Finite element methods and weak formulation. Application to linear elliptic and parabolic 1D, nods to the 2D case.
Part VI. [1]
Application to model linear and nonlinear problems.

[1] R. J. LeVeque -- Finite Difference Methods for ODEs and PDEs, Steady State and Time Dependent Problems. SIAM, Philadelphia, 2007
[2] Bertaccini, Di Fiore, Zellini, Complessita' e iterazione, Boringhieri, 2013