- Docente: Elena Loli Piccolomini
- Credits: 6
- SSD: MAT/08
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
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. Partial Differential Equations (PDE): hints.
Transport and heat equation: finite difference methods, explicit
and implicit Euler, Cranck-Nickolson.
Iterative methods for the solution of linear systems: Jacobi,
Gauss-Sidel, SOR, Conjugate Gradients, GMRES.
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