170 citations · 1.3k across the 56 of their papers we have counts for
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A Multi-Order Extension of Fractional HBVMs (FHBVMs)
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
The efficient numerical solution of fractional differential equations has been recently tackled through the definition of Fractional HBVMs (FHBVMs), a class of Runge-Kutta type met…
Analysis and implementation of collocation methods for fractional differential equations
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential…
Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code
L. Brugnano, G. Gurioli, F. Iavernaro
In this paper we report a few numerical tests by using a slight extension of the Matlab code fhbvm in [8], implementing Fractional HBVMs, a recently introduced class of numerical m…
Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
In this paper we describe the efficient numerical implementation of Fractional HBVMs, a class of methods recently introduced for solving systems of fractional differential equation…
A shooting-Newton procedure for solving fractional terminal value problems
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is parti…
A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
L. Brugnano, K. Burrage, P. Burrage +1
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vec…
An entropy-based approach for a robust least squares spline approximation
Luigi Brugnano, Domenico Giordano, Felice Iavernaro +1
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subjec…
(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…
A new framework for polynomial approximation to differential equations
Luigi Brugnano, Gianluca Frasca-Caccia, Felice Iavernaro +1
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the…
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…
Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles
Luigi Brugnano, Felice Iavernaro, Ruili Zhang
Gyrocenter dynamics of charged particles plays a fundamental role in plasma physics. In particular, accuracy and conservation of energy are important features for correctly perform…
Spectrally accurate space-time solution of Manakov systems
Luigi Barletti, Luigi Brugnano, Yifa Tang +1
In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration…
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…
Line Integral solution of Hamiltonian PDEs
Luigi Brugnano, Gianluca Frasca-Caccia, Felice Iavernaro
In this paper, we report about recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving line integral methods in t…
High-order energy-conserving Line Integral Methods for charged particle dynamics
L. Brugnano, J. I. Montijano, L. Rández
In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line…
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…
Spectrally accurate space-time solution of Hamiltonian PDEs
Luigi Brugnano, Felice Iavernaro, Juan I. Montijano +1
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral metho…
Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the "Good" Boussinesq Equation
Luigi Brugnano, Gianmarco Gurioli, Chengjian Zhang
In this paper we study the geometric solution of the so called "good" Boussinesq equation. This goal is achieved by using a convenient space semi-discretization, able to preserve t…
On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems
L. Brugnano, J. I. Montijano, L. Rández
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Va…