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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tao Liu & Stanford Shateyi, 2024. "Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem," Mathematics, MDPI, vol. 12(7), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1121-:d:1372131
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    References listed on IDEAS

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    1. Nicholas L. Georgakopoulos, 2018. "Illustrating Finance Policy with Mathematica," Quantitative Perspectives on Behavioral Economics and Finance, Palgrave Macmillan, number 978-3-319-95372-4, February.
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