170 citations · 1.3k across the 56 of their papers we have counts for
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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…
On the Existence of Energy-Preserving Symplectic Integrators Based upon Gauss Collocation Formulae
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
We introduce a new family of symplectic integrators depending on a real parameter. When the paramer is zero, the corresponding method in the family becomes the classical Gauss coll…
The Hamiltonian BVMs (HBVMs) Homepage
Luigi Brugnano, Felice Iavernaro, Donato Trigiante
Hamiltonian Boundary Value Methods (in short, HBVMs) is a new class of numerical methods for the efficient numerical solution of canonical Hamiltonian systems. In particular, their…
Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their connections with Runge-Kutta collocation methods
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. R…
Numerical comparisons between Gauss-Legendre methods and Hamiltonian BVMs defined over Gauss points
Luigi Brugnano, Felice Iavernaro, Tiziana Susca
Hamiltonian Boundary Value Methods are a new class of energy preserving one step methods for the solution of polynomial Hamiltonian dynamical systems. They can be thought of as a g…
Isospectral Property of Hamiltonian Boundary Value Methods (HBVMs) and their blended implementation
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. R…
Blended General Linear Methods based on Boundary Value Methods in the GBDF family
Luigi Brugnano, Cecilia Magherini
Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. M…