Analysis on the method of fundamental solutions for biharmonic equations

被引：7
|
作者：
Dou, Fangfang [1 ]
Li, Zi-Cai [2 ]
Chen, C. S. [3 ]
Tian, Zhaolu [4 ]
机构：
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
[3] Univ Southern Mississippi, Dept Math, Hattiesburg, MS 39406 USA
[4] Taiyuan Univ Technol, Coll Data Sci, Taiyuan, Shanxi, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 339卷
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Error analysis; Stability analysis; Biharmonic equations; Method of fundamental solutions; Trefftz methods; TREFFTZ METHOD;
D O I：
10.1016/j.amc.2018.07.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the error and stability analysis of the method of fundamental solution (MFS) is explored for biharmonic equations. The bounds of errors are derived for the fundamental solutions r(2) ln r in bounded simply-connected domains, and the polynomial convergence rates are obtained for certain smooth solutions. The bounds of condition number are also derived to show the exponential growth rates for disk domains. Numerical experiments are carried out to support the above analysis, which is the first time to provide the rigorous analysis of the MFS using r(2) ln r for biharmonic equations. (C) 2018 Elsevier Inc. All rights reserved.
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页码：346 / 366
页数：21
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