Module page
Istituzioni di Analisi Numerica
| academic year: | 2013/2014 |
| instructor: | Maurizio Falcone |
| degree course: | Mathematics for applications (magistrale) |
| type of training activity: | caratterizzante |
| credits: | 9 (72 class hours) |
| scientific sector: | MAT/08 Analisi numerica |
| teaching language: | italiano |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject:
- Numerical linear algebra
Numerical solution of linear systems. Algebraic and iterative methods. Conjugate gradient method. Iterative methods for structured matrices. Preconditioning techniques. Numerical solution of the eigenvalue problem via local and global methods. Singular value decomposition. - Numerical integration of ordinary differential equations
One-step methods. Stability, consistency and convergence. Variable step-size methods. Multistep methods: consistency and stability. A-stability. Essentials on the two point boundary value problem and its solution via finite difference methods. - Discretization of linear partial differential equations
Finite difference methods. The scalar transport equation. Euler methods, Upwind scheme, Lax-Friedrichs and Lax-Wendroff methods. Stability, consistency and convergence. Approximation of hyperbolic systems of partial differential equations and wave equation. Finite difference methods for the potential equation. Boundary conditions. Analysis of the linear systems related to different boundary conditions. Crank-Nicolson method for solving the heat equation.
A part of this course will be devoted to the analysis of algorithms and to their implementation in MATLAB.
Suggested reading:
D. Bini, M. Capovani, O. Menchi, Metodi Numerici per L'Algebra Lineare, Zanichelli, 1998.
A. Quarteroni, R. Sacco, F. Saleri, "Matematica Numerica", Springer, 2008.
Type of course: standard
Knowledge and understanding: Successful students will have theoretical knowledge related to methods of Numerical Analysis for the solution of linear systems and eigenvalue problems, for the integration of ordinary differential equations and for the approximation of linear partial differential equations. They will be also able to select, among the methods for solving the problem to be treated, the one which better fits the specific case.
Skills and attributes: Successful students will have skills and attributes related to algorithms of Numerical Analysis they learned. They will be also able to select, among the MATLAB codes for solving the problem to be treated, the one which better fits the specific case and also to bring into that code, if necessary, the modifications required to adapt it to the problem and to improve its performances.
Personal study: the percentage of personal study required by this course is the 65% of the total.