On the Solutions of Symmetric BVMs On the Solutions of Symmetric BVMs
Applied to Hamiltonian Systems

Pierluigi AMODIO
Dipartimento di Matematica
Università di Bari
Italy
Email: amodio@pascal.dm.uniba.it

We discuss a number of properties (such as, for example, the existence of a diagonal form) pertaining Hamiltonian matrices JS with

J = é
ê
ë
0
I
-I
0
 ù
ú
û
and S symmetric positive definite, and how they reflect on the solution of Hamiltonian systems and their discrete counterpart obtained by symmetric schemes.

Moreover, the solution of the linear systems arising from the application of BVMs deserves a particular attention, because the iterative schemes should be tuned in order to preserve some conservative features that are typical of Hamiltonian problems.

The question of approximating the exponential of a Hamiltonian matrix is also faced and a technique is proposed which dynamically increases the order of a given formula, in order to minimize the computational cost.

File translated from TEX by TTH, version 1.94.
On 16 Apr 2002, 17:45.