Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization

DOI10.3934/dcdss.2022016zbMath1484.47192arXiv2103.03658OpenAlexW3134022992WikidataQ114022619 ScholiaQ114022619MaRDI QIDQ2129154

Yanzhi Zhang, Yixuan Wu

Publication date: 22 April 2022

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.03658

zbMATH Keywords

fractional LaplacianLagrange basis functionsoperator factorizationfractional Poisson problemstempered fractional Laplacian

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Applications of operator theory in numerical analysis (47N40)

Related Items (1)

Error Estimates of Finite Difference Methods for the Fractional Poisson Equation with Extended Nonhomogeneous Boundary Conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Fractional Laplacian: Pohozaev identity and nonexistence results
• Ten equivalent definitions of the fractional Laplace operator
• Local elliptic regularity for the Dirichlet fractional Laplacian
• A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
• A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
• A comparative study on nonlocal diffusion operators related to the fractional Laplacian
• Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
• Fractional Schrödinger dynamics and decoherence
• A mesh-free pseudospectral approach to estimating the fractional Laplacian via radial basis functions
• What is the fractional Laplacian? A comparative review with new results
• Numerical approximations for the tempered fractional Laplacian: error analysis and applications
• Models of space-fractional diffusion: a critical review
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• The boundary Harnack principle for the fractional Laplacian
• Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
• Numerical approximation of fractional powers of regularly accretive operators
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs
• Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
• Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains
• Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
• Computing the Ground and First Excited States of the Fractional Schrödinger Equation in an Infinite Potential Well
• Finite element approximations of the nonhomogeneous fractional Dirichlet problem

This page was built for publication: Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization