求解扩散方程的非对称径向基函数配点法  

Non-symmetric Radial Basis Function Collocation Method for Solving Diffusion Equation

作　　者：王荣 许秋燕 WANG Rong;XU Qiuyan(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《应用数学》2023年第1期152-160,共9页Mathematica Applicata

基　　金：国家自然科学基金项目(12202219,12061057);宁夏青年人才托举工程项目(TJGC2019012);宁夏高等学校科学研究项目(NYG-2022-004)。

摘　　要：本文针对扩散方程,借助于Halton节点,基于径向基函数和迭代法提出一种新的无网格方法.该方法在时间层上采用全隐离散,在空间层上构造了θ-型迭代格式,然后利用径向基函数去逼近未知函数.由于本文采用紧支集径向基函数,因而导出的离散系统矩阵是稀疏的,且有较好的条件数.最后通过数值实验验证新方法的有效性.In this paper,a new meshfree method for diffusion equation is proposed based on radial basis function and iterative method using the Halton nodes.The fully implicit discretization on time layer is adopt,and θ-type iterative schemes on space layer are constructed.Then radial basis function are used to approximate unknown function.By using the compactly supported radial basis function,the discreted matrices are sparse and have better conditions.Finally,the effectiveness of the new method is verified by numerical experiments.

关 键 词：扩散方程 Kansa方法 径向基函数 θ-型迭代格式 

分 类 号：O241.82[理学—计算数学]