Learning outcomes

The course has the purpose to analyse the main numerical methods for the solution of ordinary and classical partial differential equations, from both the analytic and the computational point of view.
There is an important part in the laboratory, where the studied methods are implemented and tested.

Program

Numerical linear algebra (semiiterative methods for the solution of large ans sparse linear systems).
Ordinary differential equations: numerical methods for initial value problems, one step methods (theta-method, variable step-size Runge-Kutta, exponential integrators) and
multistep, stiff problems, stability;
boundary value problems, finite differences and finite elements methods, spectral methods (collocation and Galerkin).
Partial differential equations: classical equations (Laplace, heat, transport and waves), multidimensional finite differences methods, the method on lines.

Examination Methods

Oral and written exam