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A symmetric integrated radial basis function method for solving differential equations
Author(s) -
MaiDuy Nam,
Dalal Deepak,
Le Thi Thuy Van,
NgoCong Duc,
TranCong Thanh
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22240
Subject(s) - mathematics , radial basis function , cartesian coordinate system , boundary value problem , hermite polynomials , poisson's equation , hermite interpolation , basis function , grid , partial differential equation , interpolation (computer graphics) , mathematical analysis , meshfree methods , finite element method , geometry , computer science , animation , physics , computer graphics (images) , machine learning , artificial neural network , thermodynamics
In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.