Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1685-1704
Journal / PublicationComputers and Mathematics with Applications
Issue number5
Online published15 Dec 2017
Publication statusPublished - 1 Mar 2018


Spectral/pseudo-spectral methods based on high order polynomials have been successfully used for solving partial differential and integral equations. In this paper, we will present the use of a localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for solving 2D nonlocal problems with radial nonlocal kernels. The basic idea of the LRBF-PSM is to construct a set of orthogonal functions by RBFs on each overlapping sub-domain from which the global solution can be obtained by extending the approximation on each sub-domain to the entire domain. Numerical implementation indicates that the proposed LRBF-PSM is simple to use, efficient and robust to solve various nonlocal problems.

Research Area(s)

  • Cardinal function, Discontinuity, Nonlocal diffusion equations, Radial basis functions, Spectral/pseudo-spectral methods