A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation
Cost effectiveness; Finite difference method; Iterative methods; Partial differential equations; Computational costs; Optimal variables; Partial differential equations (PDE); Polynomial form; Radial basis functions; Rate of convergence; Shape parameters; Solution accuracy; Radial basis function netw...
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2023
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my.uniten.dspace-246592023-05-29T15:25:36Z A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation Ng Y.L. Ng K.C. Sheu T.W.H. 55812479000 55310814500 13302578200 Cost effectiveness; Finite difference method; Iterative methods; Partial differential equations; Computational costs; Optimal variables; Partial differential equations (PDE); Polynomial form; Radial basis functions; Rate of convergence; Shape parameters; Solution accuracy; Radial basis function networks Radial basis functions (RBFs) with multiquadric (MQ) kernel have been commonly used to solve partial differential equation (PDE). The MQ kernel contains a user-defined shape parameter (?), and the solution accuracy is strongly dependent on the value of this ?. In this study, the MQ-based RBF finite difference (RBF-FD) method is derived in a polynomial form. The optimal value of ? is computed such that the leading error term of the RBF-FD scheme is eliminated to improve the solution accuracy and to accelerate the rate of convergence. The optimal ? is computed by using finite difference (FD) and combined compact differencing (CCD) schemes. From the analyses, the optimal ? is found to vary throughout the domain. Therefore, by using the localized shape parameter, the computed PDE solution accuracy is higher as compared to the RBF-FD scheme which employs a constant value of ?. In general, the solution obtained by using the ? computed from CCD scheme is more accurate, but at a higher computational cost. Nevertheless, the cost-effectiveness study shows that when the number of iterative prediction of ? is limited to two, the present RBF-FD with ? by CCD scheme is as effective as the one using FD scheme. � 2019, � 2019 Taylor & Francis Group, LLC. Final 2023-05-29T07:25:36Z 2023-05-29T07:25:36Z 2019 Article 10.1080/10407790.2019.1627811 2-s2.0-85067436115 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067436115&doi=10.1080%2f10407790.2019.1627811&partnerID=40&md5=dba090f5cad733423ce429ce487e46ae https://irepository.uniten.edu.my/handle/123456789/24659 75 5 289 311 Taylor and Francis Ltd. Scopus |
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| description |
Cost effectiveness; Finite difference method; Iterative methods; Partial differential equations; Computational costs; Optimal variables; Partial differential equations (PDE); Polynomial form; Radial basis functions; Rate of convergence; Shape parameters; Solution accuracy; Radial basis function networks |
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55812479000 |
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55812479000 Ng Y.L. Ng K.C. Sheu T.W.H. |
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Article |
| author |
Ng Y.L. Ng K.C. Sheu T.W.H. |
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Ng Y.L. Ng K.C. Sheu T.W.H. A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| author_sort |
Ng Y.L. |
| title |
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| title_short |
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| title_full |
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| title_fullStr |
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| title_full_unstemmed |
A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation |
| title_sort |
new higher-order rbf-fd scheme with optimal variable shape parameter for partial differential equation |
| publisher |
Taylor and Francis Ltd. |
| publishDate |
2023 |
| _version_ |
1806424126020124672 |