29 citations · 174 across the 23 of their papers we have counts for
23 papers
On the use of the principle of maximum entropy to improve the robustness of bivariate spline least-squares approximation
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distributi…
Does the fluid-static equilibrium of a self-gravitating isothermal sphere of van der Waals' gas present multiple solutions?
Domenico Giordano, Pierluigi Amodio, Felice Iavernaro +1
We take up the investigation we left in the future-work stack in Giordano \textit{et al.} [``Fluid statics of a self-gravitational isothermal sphere of van der Waals' gas,'' Phys.…
Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas
Domenico Giordano, Pierluigi Amodio, Felice Iavernaro +3
We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravit…
A didactically motivated reexamination of a particle's quantum mechanics with square-well potentials
Domenico Giordano, Pierluigi Amodio, Felice Iavernaro
We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omissio…
(Spectral) Chebyshev collocation methods for solving differential equations
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value…
A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials
P. Amodio, L. Brugnano, F. Iavernaro
In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t.…
Continuous-Stage Runge-Kutta approximation to Differential Problems
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary V…
Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
In this paper we are concerned with numerical methods for the one-sided event location in discontinuous differential problems, whose event function is nonlinear (in particular, of…
Arbitrarily high-order energy-conserving methods for Hamiltonian problems with quadratic holonomic constraints
P. Amodio, L. Brugnano, G. Frasca-Caccia +1
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within…
Arbitrarily high-order energy-conserving methods for Poisson problems
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
In this paper we are concerned with energy-conserving methods for Poisson problems, which are effectively solved by defining a suitable generalization of HBVMs, a class of energy-c…
Complement to our article: "Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics"
Domenico Giordano, Pierluigi Amodio
We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimen…
Implementation of the PaperRank and AuthorRank indices in the Scopus database
Pierluigi Amodio, Luigi Brugnano, Filippo Scarselli
We implement the PaperRank and AuthorRank indices introduced in [Amodio & Brugnano, 2014] in the Scopus database, in order to highlight quantitative and qualitative information tha…
Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics
Domenico Giordano, Pierluigi Amodio
We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt regarding whether or not the herm…
On the use of the Infinity Computer architecture to set up a dynamic precision floating-point arithmetic
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro +1
We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity A…
Mathematical aspects relative to the fluid statics of a self-gravitating perfect-gas isothermal sphere
Pierluigi Amodio, Domenico Giordano, Felice Iavernaro +4
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The…
A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
In recent years, the class of energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) has been devised for numerically solving Hamiltonian problems. In this shor…
Fluid statics of a self-gravitating perfect-gas isothermal sphere
Domenico Giordano, Pierluigi Amodio, Felice Iavernaro +4
We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical t…
Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
Recently, the numerical solution of stiffly/highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in tim…
Variable-step finite difference schemes for the solution of Sturm-Liouville problems
Pierluigi Amodio, Giuseppina Settanni
We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its n…
Energy-conserving methods for Hamiltonian Boundary Value Problems and applications in astrodynamics
P. Amodio, L. Brugnano, F. Iavernaro
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along whi…
On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
P. Amodio, Yu. Blinkov, V. Gerdt +1
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these appro…
Recent advances in bibliometric indexes and the PaperRank problem
Pierluigi Amodio, Luigi Brugnano
Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very d…
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…