A one-stage meshless method for nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients

被引：4

作者：

Xiong, Xiangtuan ^{[1
]}

Li, Ming ^{[2
]}

Wang, M. Q. ^{[2
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou, Peoples R China

[2] Taiyuan Univ Technol, Coll Math, Taiyuan, Peoples R China

来源：

JOURNAL OF ENGINEERING MATHEMATICS | 2013年 / 80卷 / 01期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Cauchy problem; Ill-posed; Meshless; Regularization; COMPUTATIONAL FLUID-DYNAMICS; DATA APPROXIMATION SCHEME; ILL-POSED PROBLEMS; FUNDAMENTAL SOLUTION; L-CURVE; REGULARIZATION; MULTIQUADRICS; BOUNDARY; ELEMENT;

D O I：

10.1007/s10665-012-9578-5

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A one-stage meshless method is devised for solving Cauchy boundary value problems of elliptic partial differential equations (PDEs) with variable coefficients. The main idea is to approximate an unknown solution using a linear combination of fundamental solutions and radial basis functions. Compared with the two-stage method of particular solution, the proposed method can deal with more general elliptic PDEs with variable coefficients. Several numerical results in both two- and three-dimensional space show that our proposed method is accurate and effective.

引用

页码：189 / 200

页数：12

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