|Course title||Time discretization techniques for large ODE systems|
|Institution||Politecnico di Milano|
|Course address||Via Bonardi 9|
|Minimum year of study||4th year|
|Minimum level of English||Good|
|Minimum level of French||None|
|Professor responsible||L. Bonaventura|
|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.|