Luigi Brugnano

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Abstract: Recently, a new family of integrators (Hamiltonian Boundary Value Methods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy in the non-polynomial case. We settle the definition and the theory of such methods in a more general(More)
When numerically integrating canonical Hamiltonian systems, the long-term conservation of some of its invariants, for example the Hamiltonian function itself, assumes a central role. The classical approach to this problem has led to the definition of symplectic methods, among which we mention Gauss–Legendre collocation formulae. Indeed, in the continuous(More)
Abstract. The correct formulation of numerical models for free-surface hydrodynamics often requires the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In so doing one may prevent the development of unrealistic negative water depths. The resulting piecewise linear systems are equivalent to(More)
AIM This multicentre study, based on the largest patient population ever published, aims to evaluate the efficacy of Doppler-guided transanal haemorrhoidal dearterialization (THD Doppler) in the treatment of symptomatic haemorrhoids and to identify the factors predicting failure for an effective mid-term outcome. METHOD Eight hundred and three patients(More)
Keywords: Ordinary differential equations Runge–Kutta methods One-step methods Hamiltonian problems Hamiltonian Boundary Value Methods Energy preserving methods Symplectic methods Energy drift a b s t r a c t In this paper, we provide a simple framework to derive and analyse a class of one-step methods that may be conceived as a generalization of the class(More)
We discuss the efficient implementation of Hamiltonian BVMs (HBVMs), a recently introduced class of energy preserving methods for canonical Hamiltonian systems (see [2] and references therein), via their blended formulation. We also discuss the case of separable problems, for which the structure of the problem can be exploited to gain efficiency.
We introduce a new family of symplectic integrators for canonical Hamiltonian systems. Each method in the family depends on a real parameter α. When α = 0 we obtain the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null α, the corresponding method remains symplectic and has order 2s−2;(More)
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 numerical solution of linear complementarity problems and in the numerical solution of free-surface problems. In particular, we here study their application to the numerical solution(More)
The correct numerical modeling of free-surface hydrodynamic problems often requires to have the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In doing so, one may fulfill relevant physical constraints. The existence, the uniqueness, and two constructive iterative methods to solve a(More)