Numerical solution of the Sturm-Liouville problem with local RBF-based differential quadrature collocation method

被引：11
作者：
Shen, Quan [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 02期
关键词：
local RBF-based differential quadrature; radial basis function; globally supported radial basis function; Sturm-Liouville problem; collocation method; multiquadric; finite difference method; meshless; DATA APPROXIMATION SCHEME; RADIAL BASIS FUNCTIONS; SCATTERED DATA; INTERPOLATION; MULTIQUADRICS;
D O I：
10.1080/00207160903370180
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we present a local RBF-based differential quadrature (LRBFDQ) collocation method for the Sturm-Liouville problem with Dirichlet, Neumann, mixed, periodic, and semi-periodic boundary conditions. Compared with the globally supported RBF (GSRBF) collocation method, this novel method approximates the derivatives by RBF interpolation using a small set of nodes in the neighbourhood of any collocation node. Less computational time is needed than the GSRBF collocation method. Compared with the GSRBF collocation method and the finite difference method (FDM), numerical results demonstrate the accuracy and easy implementation of the LRBFDQ collocation method.
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收藏
页码：285 / 295
页数：11
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