Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
type: Item
instance of: scholarly article
title: Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
zbMATH Open document ID: 1409.65111
author: Gabriel Acosta
author: Juan Pablo Borthagaray
author: O. P. Bruno
author: Martín Maas
published in: Mathematics of Computation
publication date: 2018-04-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1608.08443
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 6864186
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: hypersingular integral equations
zbMATH Keywords: high-order numerical methods
zbMATH Keywords: Gegenbauer polynomials
describes a project that uses: FastGaussQuadrature
MaRDI profile type: Publication
OpenAlex ID: W2511053218
arXiv ID: 1608.08443
cites work: Large \(s\)-harmonic functions and boundary blow-up solutions for the fractional Laplacian
cites work: A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
cites work: Gevrey regularity for integro-differential operators
cites work: Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
cites work: Q4112938
cites work: A concave-convex elliptic problem involving the fractional Laplacian
cites work: Q4300595
cites work: An Extension Problem Related to the Fractional Laplacian
cites work: Financial Modelling with Jump Processes
cites work: Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
cites work: The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
cites work: Hitchhiker's guide to the fractional Sobolev spaces
cites work: Fractional Laplace operator and Meijer G-function
cites work: Numerical approximation of the fractional Laplacian via \(hp\)-finite elements, with an application to image denoising
cites work: Nonlocal Operators with Applications to Image Processing
cites work: Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
cites work: Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
cites work: Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
cites work: Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
cites work: Q4791752
cites work: Natural and Modified Forms of Distributed-Order Fractional Diffusion Equations
cites work: Linear integral equations
cites work: Fractional Cable Equation Models for Anomalous Electrodiffusion in Nerve Cells: Finite Domain Solutions
cites work: A generalized Calderón formula for open-arc diffraction problems: theoretical considerations
cites work: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
cites work: A PDE approach to fractional diffusion in general domains: a priori error analysis
cites work: The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
cites work: Q5526189
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: On the spectrum of two different fractional operators
cites work: Integral equation methods in potential theory. II
cites work: Q4061445
cites work: From the long jump random walk to the fractional Laplacian
cites work: On exponential convergence of Gegenbauer interpolation and spectral differentiation
cites work: On integral equations of the first kind with logarithmic kernels
cites work: Sharp error bounds for Jacobi expansions and Gegenbauer-Gauss quadrature of analytic functions
DOI: 10.1090/MCOM/3276
description: scientific article; zbMATH DE number 6864186