Now showing items 1-7 of 7

• #### Numerical approximation of the fractional Laplacian on R using orthogonal families ﻿

(2020-12-01)
In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the F12 Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the complex Higgins functions, the complex ...
• #### On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion ﻿

(2019-09-03)
In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ...
• #### On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation ﻿

(2018-06-28)
In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...
• #### A pseudospectral method for the one-dimensional fractional Laplacian on R ﻿

(2021-01-15)
In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ...
• #### The Vortex Filament Equation as a Pseudorandom Generator ﻿

(2015-08-01)
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ...
• #### Vortex filament equation for a regular polygon ﻿

(2014-12-31)
In this paper, we study the evolution of the vortex filament equation,$$X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ...
• #### Vortex Filament Equation for a regular polygon in the hyperbolic plane ﻿

(2020-07-09)
The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and ...