35433 - NUMERICAL METHODS

Conoscenze e abilità da conseguire

At the end of the course, students know basic numerical methods for evolutive ordinary and partial differential problems, together with their main theoretical and computational properties. In particular, students are able to analyze the properties of numerical methods; constructively examine corresponding computational results; advance their scientific computing education in higher level courses; employ the acquired numerical skills in a variety of application areas.

Contenuti

 

• Numerical solution of non-linear systems
• Gaussian quadrature formulas
• Numerical solution of Ordinary Differential Equations
  • Initial value problems
    • Onestep-multistep methods
    • Convergence, stability
  • Boundary value problems
    • Shooting Method
    • Finite difference method
    • Galerkin’s Method
• Time dependent Partial Differential Equations: Method of Lines

Prerequisites

- Matlab programming

- Floating point arithmetic.
- Numerical methods for the solution of linear systems;

- Numerical methods for the solution of nonlinear equations.
- Data approximation: polynomial and piecewise polynomial functions; interpolation and least-squares approximation.
- Numerical integration: Newton-Cotes quadrature formulas.

Testi/Bibliografia

• Course Lecture notes

• U. Ascher and L. Petzold. Computer methods for ordinary differential equations and differential-algebraic equations. SIAM, 1998.
• D.F. Griffths and D.J. Higham. Numerical Methods for Ordinary Differential Equations: Initial Value Problems. Springer, 2010.
• Randal J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, 2007.
• Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. Numerical Mathematics (Texts in Applied Mathematics). Springer-Verlag, Berlin, Heidelberg, 2006.
• H.B.Keller. Numerical Methods for Two-Point Boundary Value Problems. Dover Ed., 2018.

Metodi didattici

Classroom lectures and computer laboratory

Modalità di verifica e valutazione dell'apprendimento

• Laboratory Project

• Written test and oral discussion.

Strumenti a supporto della didattica

e-learning platform: Virtuale

Orario di ricevimento

Consulta il sito web di Fabiana Zama