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

被引：1

作者：

Liu, Tao ^{[1
]}

Shateyi, Stanford ^{[2
]}

机构：

[1] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Peoples R China

[2] Univ Venda, Sch Math & Nat Sci, Dept Math & Appl Math, P Bag X5050, ZA-0950 Thohoyandou, South Africa

来源：

MATHEMATICS | 2024年 / 12卷 / 07期

关键词：

radial basis function (RBF); convergence order; Hermite finite difference (HFD); analytical weights; fractional PDE;

D O I：

10.3390/math12071121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：13