The closed-form particular solutions for Laplace and biharmonic operators using a Gaussian function

被引：22
|
作者：
Lamichhane, A. R. [1 ]
Chen, C. S. [1 ]
机构：
[1] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA
来源：
APPLIED MATHEMATICS LETTERS | 2015年 / 46卷
关键词：
Radial basis functions; Particular solution; Meshless method; Method of particular solution; Localized method of approximate particular solutions; Gaussian RBF; HELMHOLTZ-TYPE;
D O I：
10.1016/j.aml.2015.02.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Particular solutions play a critical role in solving inhomogeneous problems using boundary methods such as boundary element methods or boundary meshless methods. In this short article, we derive the closed-form particular solutions for the Laplace and biharmonic operators using the Gaussian radial basis function. The derived particular solutions are implemented numerically to solve boundary value problems using the method of particular solutions and the localized method of approximate particular solutions. Two examples in 2D and 3D are given to show the effectiveness of the derived particular solutions. (C) 2015 Elsevier Ltd. All rights reserved.
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页码：50 / 56
页数：7
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