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### Numerical Modeling

Professors:
Della Croce Lucia
Year:
2015/2016
Course code:
502234
ECTS:
6
SSD:
MAT/08
DM:
270/04
Lessons:
56
Period:
I semester
Language:
Italian

#### Objectives

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.

#### Teaching methods

Lectures and exercises in the Computer Lab

#### Examination

Oral exam with discussion of elaborates Matlab

#### Prerequisites

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

#### Syllabus

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.

#### Bibliography

McGraw-Hill, 1995.
A. Quarteroni: "Modellistica Numerica per problemi differenziali", Springer,

Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602