Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Tao Liu and Stanford Shateyi ()
Additional contact information
Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2024, vol. 12, issue 7, 1-13

Abstract: An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems.

Keywords: radial basis function (RBF); convergence order; Hermite finite difference (HFD); analytical weights; fractional PDE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/7/1121/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/7/1121/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:7:p:1121-:d:1372131

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().