A symmetric integrated radial basis function method for solving differential equations
Article
Article Title | A symmetric integrated radial basis function method for solving differential equations |
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ERA Journal ID | 344 |
Article Category | Article |
Authors | Mai-Duy, Nam (Author), Dalal, Deepak (Author), Le, Thi Thuy Van (Author), Ngo-Cong, Duc (Author) and Tran-Cong, Thanh (Author) |
Journal Title | Numerical Methods for Partial Differential Equations |
Journal Citation | 34 (3), pp. 959-981 |
Number of Pages | 23 |
Year | 2018 |
Place of Publication | United States |
ISSN | 0749-159X |
1098-2426 | |
Digital Object Identifier (DOI) | https://doi.org/10.1002/num.22240 |
Web Address (URL) | https://onlinelibrary.wiley.com/doi/full/10.1002/num.22240 |
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. |
Keywords | compact local approximation, extended precision, flat radial basis function, global approximation, Hermite interpolation, integrated radial basis function |
ANZSRC Field of Research 2020 | 490302. Numerical analysis |
490399. Numerical and computational mathematics not elsewhere classified | |
490199. Applied mathematics not elsewhere classified | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | Computational Engineering and Science Research Centre |
School of Mechanical and Electrical Engineering | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q4z88/a-symmetric-integrated-radial-basis-function-method-for-solving-differential-equations
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