Course code POLI11
Course title Time discretization techniques for large ODE systems
Institution Politecnico di Milano
Course address Via Bonardi 9
City Milan
Minimum year of study 4th year
Minimum level of English Good
Minimum level of French None
Key words
Language English
Professor responsible L. Bonaventura
Telephone +390223994600
Fax +390223994568
Participating professors L. Bonaventura
Number of places Minimum: 5, Maximum: 20, Reserved for local students: 0
Objectives The course will present advanced time discretization
techniques that allow for an efficient numerical solution
of large systems of ordinary differential equations
resulting from the spatial discretization of PDEs.
All the theoretical topics will be complemented by practical
sessions based on the application of MATLAB implementations
of the various algorithms presented in the course.
Reference literature and the course notes will be made available. 
Programme to be followed 1) Review of fundamental concepts on numerical  methods for time discretization of evolutionary  problems. Examples of classical multistage and  multistep methods for the  solution of ODE systems. Some model problems.

2) Implicit methods and robust techniques for stiff systems:  BDF, Rosenbrock-Wanner methods.

3) Methods for second order ODE systems:  the Newmark and the generalized alpha-method.

4) Introduction to Runge Kutta and Rosenbrock exponential integrators. 
Prerequisites Good MATLAB skills, basic courses on Calculus, Numerical Methods and Ordinary Differential Equations
Course exam Small programming project in MATLAB for the solution of relevant test problems by the methods introduced in the course.