72764 - NUMERICAL METHODS

Scheda insegnamento

Anno Accademico 2018/2019

Conoscenze e abilità da conseguire

A successful learner from this course will be able to: a) deal with numerical analysis topics such as: accuracy, truncation and round-off errors, condition numbers, convergence, stability, curve-fitting, interpolation, numerical differentiation and integration, numerical linear algebra; b) deal with numerical methods for solving ordinary and partial differential equations, with finite difference and finite element methods for parabolic and elliptic partial differential equations, applications of computer programs to case studies derived from civil engineering practice.

Programma/Contenuti

First Part

  • Key idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
  • Numerical Linear Algebra: direct and iterative methods for linear systems.

  • Solution to single equations and multiple non-linear equations.
  • Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.

  • Numerical differentiation.

    Exercises with Matlab on the previous topics.

 

Second Part

- Numerical Integration (quadrature):

- Newton-Cotes quadrature formulas

- Gaussian quadrature formulas

- Numerical solution of Partial Differential Equations (PDEs) by the Finite Difference Method:

- Elliptic PDEs: Poisson Equation

- Parabolic PDEs: Heat Equation

- Hyperbolic PDEs: Transport (Advection) Equation

Testi/Bibliografia

Some useful course materials for this course can be found at the web page piattaforma iol

https://iol.unibo.it/

or

http://www.dm.unibo.it/~sgallari

You can find the material for this course in many books on Numerical Analysis such as

  1. A. Quarteroni, F. Saleri, P. Gervasio, Scientific Computing with Matlab and Octave, Springer.
  2. A. Quarteroni, R. Sacco and F. Saleri
    Numerical Mathematics Springer.

For the second Part

- A. Quarteroni, Numerical Models for Differential Problems (3rd Edition), Springer International Publishing, 2017.

Metodi didattici

The course involves practical work based on computational tools such as Matlab.

Modalità di verifica dell'apprendimento

Assessment is based on assignments of project works and oral discussions.

Strumenti a supporto della didattica

Lectures, exercises, laboratory activities in Matlab.

Orario di ricevimento

Consulta il sito web di Fiorella Sgallari

Consulta il sito web di Alessandro Lanza