偏微分方程边值问题的数值解法研究  

Study on the numerical method for the boundary value problems of partial differential equations

作　　者：王福章 郭玄玄[2] 周童 WANG Fuzhang;GUO Xuanxuan;ZHOU Tong(School of Mathematical and Statistics,Xuzhou University of Technology,Xuzhou 221018,China;School of Mathematical Sciences,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]徐州工程学院数学与统计学院,江苏徐州221018 [2]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《高师理科学刊》2021年第1期13-15,20,共4页Journal of Science of Teachers＇College and University

摘　　要：利用椭圆型偏微分方程边值问题的数学模型,对Kansa法数值模拟进行了探讨.考虑切比雪夫节点作为数值模拟过程中的配点,与传统Kansa法和解析解的结果进行了对比研究.数值结果表明,对于椭圆型偏微分方程边值问题,基于切比雪夫节点的Kansa法数值模拟具有令人更为满意的结果.Using the mathematical model of the boundary value problems of elliptic partial differential equation,the numerical simulation of Kansa′s method was discussed.Considering the Chebyshev node as the collocation point in the process of numerical simulation,it was compared with the results of traditional Kansa′s method and analytical solution.The numerical results showed that the numerical simulation based on the Chebyshev node of Kansa′s method has more satisfactory results for the boundary value problems of elliptic partial differential equations.

关 键 词：径向基函数 偏微分方程 无网格法 Kansa法 

分 类 号：O242.1[理学—计算数学]