The course is intended to integrate and extend the knowledge achieved by the course of numerical analysis, with particular attention to the solution of boundary value problems. Fundamental objective is to present the various techniques of numerical modeling, both revisiting the classic algorithms of numerical analysis, and introducing new methods of approximation.

Lectures and exercises in the Computer Lab

Oral exam with discussion of elaborates Matlab

Numerical Analysis and basic knowledge of MATLAB language are the prerequisites of the course of Numerical Modeling.

We introduce numerical algorithms for solving differential initial and boundary values problems​​.

In particular, we will study the finite difference methods of approximation. Moreover we provide 'a variational formulation of elliptic problems of type diffusion and advection-diffusion for a finite element approximation.

Will be part of the course elements of language MATLAB.



Initial value problems:

- One step numerical algorithms for the solution of the Cauchy problem;

- Methods multisteps;

- One-step methods of higher order;

- Convergence of one-step methods;

- 0-established', consistency and convergence of multisteps methods;

- Absolute stability ', stiff problems.

Boundary value problems;

- Diffusion models, existence and uniqueness' of the solution of the problem of

   diffusion-reaction with boundary conditions of Dirichlet and Neumann type;

- Numerical methods for solving boundary value problems, method of Shooting;

- Finite difference method, existence and uniqueness' of the solution of the

   discrete problem of diffusion-reaction;

- Problem-diffusion transport, wind-up method;

- Evolutionary problems, heat equation, Theta-method;

- Variational methods, weak formulation of the problem of diffusion-reaction;

- Bilinear forms and Galerkin approximation method;

- Consistency and convergence of the Galerkin method.

McGraw-Hill, 1995.

A. Quarteroni: "Modellistica Numerica per problemi differenziali", Springer,