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A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional -Laplacian of functions defined on
Loïc Constantin, Carlota M. Cuesta, Francisco de la Hoz
Given a function defined on , its fractional -Laplacian is given by $$(-Δ)_p^su(\vec x)=C_1(n,s,p)\int_{\mathbb R^n}\frac{|u(\vec x)-u(\vec y)|^{p-2}(u(\vec x)-…
A Non-Recursive, Dimension-Independent Schur-Decomposition Algorithm for -Dimensional Sylvester Tensor Equations
Carlota M. Cuesta, Francisco de la Hoz
In this paper we present a non-recursive direct solver, based on the Bartels-Stewart algorithm, for -dimensional Sylvester tensor equations. The method relies only on Schur deco…
Numerical Approximation of Riesz-Feller Operators on
Carlota M. Cuesta, Francisco de la Hoz, Ivan Girona
In this paper, we develop an accurate pseudospectral method to approximate numerically the Riesz-Feller operator on , where , and $|γ|\le\min\{α, 2 -…
Numerical computation of the half Laplacian by means of a fast convolution algorithm
Carlota M. Cuesta, Francisco de la Hoz, Ivan Girona
In this paper, we develop a fast and accurate pseudospectral method to approximate numerically the half Laplacian of a function on , which is equivalent to…
A fast convolution method for the fractional Laplacian in
Jorge Cayama, Carlota M. Cuesta, Francisco de la Hoz +1
In this article, we develop a new method to approximate numerically the fractional Laplacian of functions defined on , as well as some more general singular integrals. A…
Vortex Filament Equation for a regular polygon in the hyperbolic plane
Francisco de la Hoz, Sandeep Kumar, Luis Vega
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…