presso Sala Conferenze “F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il Dott. Gianluca Frasca Caccia
(Università di Firenze)
terrà una conferenza dal titolo:
"Hamiltonian Boundary Value Methods (HBVMs) and their efficient
implementation"
ABSTRACT:
One of the main features when dealing with Hamiltonian systems is the conservation of energy. In this talk I will expose the main fact about a family of conservative Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) for the efficient numerical integration of these problems. These methods yield exact conservation for polynomial energy of arbitrarily high degree and an at least "practical" conservation for non polynomial energy. We will also discuss about the efficient implementation of HBVMs by means of two different procedures: the "blended" implementation and a new iterative procedure based on a particular triangular splitting of the corresponding Butcher's matrix. The linear convergence analysis of these two procedures exhibits excellent properties that make these procedures more efficient than a classical fixed point iteration for stiff problems. A few numerical tests confirming all the theoretical findings will be shown.