Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D

被引：0

作者：

Lamichhane, Anup ^{[1
]}

Ghimire, Balaram Khatri ^{[2
]}

Dangal, Thir ^{[3
]}

机构：

[1] Ohio Northern Univ, Sch Sci Technol & Math, Ada, OH 45810 USA

[2] Alabama State Univ, Dept Math & Comp Sci, Montgomery, AL 36101 USA

[3] Augusta Univ, Dept Math, Augusta, GA 30912 USA

来源：

MATHEMATICS | 2023年 / 11卷 / 22期

关键词：

augmented polynomials; localized collocation method; oscillatory radial basis functions; particular solutions; APPROXIMATE PARTICULAR SOLUTIONS;

D O I：

10.3390/math11224690

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale problems, but this method is numerically less accurate. In this paper, we propose a numerical scheme to improve the accuracy of the L-ORBFs by adding low-degree polynomials in the localized collocation process. The numerical results validate that the proposed numerical scheme is highly accurate and clearly outperforms the results of the L-ORBFs.

引用

页数：15

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