04524 - Numerical Analysis

Learning outcomes

At the end of the course, the student has a deep knowledge of the numerical aspects of the mathemathics in the applications.

Course contents

Numerical methods for the solution of differential problems.
1. Initial Value Problems (IVP). Linear Multistep methods: consistence, zero-stability,convergence. One step Runge-Kutta methods, multistep Adams metods, predictor.corrector methods.
2. Boundary Value problems (BVP) in one dimension. Finitre difference methods explicit and implicit. Spectral methods.
3. Discrete Inverse problems: ill-conditioning, regulariization techniques. Examples.

Exercises in Matlab or Octave on the previous topics.

Readings/Bibliography

1)A. Quarteroni, Numerical models for differential problems, Springer.

2)A. Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer.

Teaching methods

Frontal lessons and exercises in the Computer Laboratory. The exercises consist in numerical simulations of the methods analysed during the lessons. They are guided by the teacher during the laboratory time. The student should individually complete the assigned exercises and finally give them up to the teacher before the end of the course.

Assessment methods

The exam consists in an oral discussion on the topics delaed with in the lessons and on the resolution of the assigned exercises.

Teaching tools

Slides

Links to further information

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

Office hours

See the website of Elena Loli Piccolomini