The local Kansa's method for solving Berger equation

被引：9
作者：
Yang, Jingyu [1 ]
Liu, Xiaofeng [1 ]
Wen, P. H. [1 ,2 ]
机构：
[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Peoples R China
[2] Univ London, Sch Engn & Mat Sci, London E1 4NS, England
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2015年 / 57卷
关键词：
Berger equation; RBF collocation methods; Matern function; MQ; Shape parameter; Local Kansa's method; Leave-One-Out-Cross-Validation; OPTIMAL SHAPE-PARAMETERS; APPROXIMATION;
D O I：
10.1016/j.enganabound.2015.03.005
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we present the local Kansa's method using radial basis functions (RBFs) to solve Berger equation which is a fourth order partial differential equation. To overcome the difficulty of solving higher order differential equations using localized RBF methods, we split the given equation into two second order partial differential equations. Furthermore, we use Matern function and normalized MQ as basis functions and make a comparison between the two radial basis functions in terms of accuracy and stability. LOOCV (Leave-One-Out-Cross-Validation) is used to find a good shape parameter of MQ and Matem function. To demonstrate the effectiveness of the local Kansas method for solving Berger equation, three examples are given. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：16 / 22
页数：7
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