A mesh-free pseudospectral approach to estimating the fractional Laplacian via radial basis functions

DOI10.1016/j.jcp.2019.02.015zbMath1452.65374OpenAlexW2921009460MaRDI QIDQ2221362

Spencer A. Rosenfeld, Joel A. Rosenfeld, Warren E. Dixon

Publication date: 26 January 2021

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.02.015

zbMATH Keywords

pseudospectral methodsfractional calculusfractional Poisson equationfractional Laplacianmesh-free methodsWendland RBFs

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11)

Related Items (13)

Numerical methods for nonlocal and fractional models ⋮ Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization ⋮ Arbitrary order recursive formulation of meshfree gradients with application to superconvergent collocation analysis of Kirchhoff plates ⋮ Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation ⋮ On spectral polar fractional Laplacian ⋮ On the fractional Laplacian of some positive definite kernels with applications in numerically solving the surface quasi-geostrophic equation as a prominent fractional calculus model ⋮ Neural Network Method for Integral Fractional Laplace Equations ⋮ A hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative ⋮ An accurate numerical technique for fractional oscillation equations with oscillatory solutions ⋮ Variable-order fractional Laplacian and its accurate and efficient computations with meshfree methods ⋮ A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs ⋮ Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis ⋮ IMEX Hermite--Galerkin Spectral Schemes with Adaptive Time Stepping for the Coupled Nonlocal Gordon-Type Systems in Multiple Dimensions

Uses Software

• Matlab

Cites Work

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