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A new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equation

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dc.citedby4
dc.contributor.authorNg Y.L.en_US
dc.contributor.authorNg K.C.en_US
dc.contributor.authorSheu T.W.H.en_US
dc.contributor.authorid55812479000en_US
dc.contributor.authorid55310814500en_US
dc.contributor.authorid13302578200en_US
dc.date.accessioned2023-05-29T07:25:36Z
dc.date.available2023-05-29T07:25:36Z
dc.date.issued2019
dc.descriptionCost 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 networksen_US
dc.description.abstractRadial 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.en_US
dc.description.natureFinalen_US
dc.identifier.doi10.1080/10407790.2019.1627811
dc.identifier.epage311
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85067436115
dc.identifier.spage289
dc.identifier.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85067436115&doi=10.1080%2f10407790.2019.1627811&partnerID=40&md5=dba090f5cad733423ce429ce487e46ae
dc.identifier.urihttps://irepository.uniten.edu.my/handle/123456789/24659
dc.identifier.volume75
dc.publisherTaylor and Francis Ltd.en_US
dc.sourceScopus
dc.sourcetitleNumerical Heat Transfer, Part B: Fundamentals
dc.titleA new higher-order RBF-FD scheme with optimal variable shape parameter for partial differential equationen_US
dc.typeArticleen_US
dspace.entity.typePublication
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