170 citations · 651 across the 13 of their papers we have counts for
13 papers
A note on the efficient implementation of Hamiltonian BVMs
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems, via their blended f…
The Lack of Continuity and the Role of Infinite and Infinitesimal in Numerical Methods for ODEs: the Case of Symplecticity
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
When numerically integrating canonical Hamiltonian systems, the long-term conservation of some of its invariants, among which the Hamiltonian function itself, assumes a central rol…
A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
In this paper, we provide a simple framework to derive and analyse several classes of effective one-step methods. The framework consists in the discretization of a local Fourier ex…
Numerical comparisons among some methods for Hamiltonian problems
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.
Energy and quadratic invariants preserving integrators of Gaussian type
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
Recently, a whole class of evergy-preserving integrators has been derived for the numerical solution of Hamiltonian problems. In the mainstream of this research, we have defined a…
Numerical Solution of ODEs and the Columbus' Egg: Three Simple Ideas for Three Difficult Problems
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
On computers, discrete problems are solved instead of continuous ones. One must be sure that the solutions of the former problems, obtained in real time (i.e., when the stepsize h…