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Parallel Factorizations in Numerical Analysis
Pierluigi Amodio, Luigi Brugnano
In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of para…
Iterative solution of piecewise linear systems for the numerical solution of obstacle problems
Luigi Brugnano, Alessandra Sestini
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the nume…
Fifty Years of Stiffness
Luigi Brugnano, Francesca Mazzia, Donato Trigiante
The notion of stiffness, which originated in several applications of a different nature, has dominated the activities related to the numerical treatment of differential problems fo…
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
Recently, a new family of integrators (Hamiltonian Boundary ValueMethods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian sys…
Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. F…