圆锥型径向基函数的配点法及其应用  

Collocation Points for the Conical Radial Basis Function Method and their Application

作　　者：郭玄玄 王福章[1,2] GUO Xuanxuan;WANG Fuzhang(School of Mathematical Sciences,Huaibei Normal University,Huaibei Anhui 235000,China;College of Arts and Sciences,Suqian College,Suqian Jiangsu 223800,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]宿迁学院文理学院,江苏宿迁223800

出　　处：《海南热带海洋学院学报》2020年第5期76-79,共4页Journal of Hainan Tropical Ocean University

基　　金：安徽省自然科学基金项目(1908085QA09);安徽省高校自然科学研究(重点)项目(KJ2019A0591)。

摘　　要：针对拉普拉斯控制方程边值问题的数学模型,用圆锥型径向基函数配点法进行数值模拟.用切比雪夫节点作为数值模拟过程中的配点,与传统圆锥型径向基函数配点法和解析解的结果进行了对比,数值结果表明:利用切比雪夫节点的圆锥型径向基函数配点法模拟椭圆型偏微分方程边值问题达到更好的结果,为其理论研究奠定基础.Based on the elliptic partial differential equations,the conical radial basis function method was investigated.During the solution process,Chebyshev points,combined with the conical radial basis function method,were introduced.Numerical results,which were compared with the traditional conical radial basis function method as well as with analytical solutions,show that the improved conical radial basis function method—a foundation for the theoretical research—is superior to the traditional Kansa’s method in terms of solution accuracy and boundary improvement.

关 键 词：径向基函数 偏微分方程 无网格法 边值问题 

分 类 号：O242.1[理学—计算数学]