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- Title
A symmetric integrated radial basis function method for solving differential equations.
- Authors
Mai‐Duy, Nam; Dalal, Deepak; Le, Thi Thuy Van; Ngo‐Cong, Duc; Tran‐Cong, Thanh
- Abstract
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.
- Subjects
RADIAL basis functions; HERMITE polynomials; MESHFREE methods; POISSON processes; DIFFERENTIAL equations
- Publication
Numerical Methods for Partial Differential Equations, 2018, Vol 34, Issue 3, p959
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22240