Numerical methods for differential equations (2013/2014)
Scientific Disciplinary Sector (SSD)
MAT/08 - NUMERICAL ANALYSIS
The teaching is organized as follows:
The course has the purpose to analyze 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.
It is highly recommended to have attended the course Numerical analysis with laboratory.
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.
After a first written part (solution in Matlab/Octave of some exercises in laboratory) there is an oral exam, to be due within the same session.