一类椭圆型Dirichlet边值问题的高精度Richardson外推法  

A High-Precision Richardson Extrapolation Method for a Class of Elliptic Dirichlet Boundary Value Calculation

作　　者：李曹杰 张海湘 杨雪花 LI Caojie;ZHANG Haixiang;YANG Xuehua(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2024年第1期91-97,104,共8页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(12226340,12226337,12126321);湖南省自然科学基金资助项目(2022JJ50083);湖南省教育厅优秀青年基金资助项目(21B0550)。

摘　　要：针对椭圆型偏微分方程,先建立四阶和六阶精度的紧致差分格式,在此基础上用Richardson外推法,得到其六阶和八阶精度的外推差分格式。并通过两个Poisson方程算例,验算已建立的差分格式。数值算例结果表明,基于紧致差分格式的Richardson外推法能够得到有效的、健壮的高精度数值解。In view of the calculation of elliptic partial differential equations,compact difference schemes with fourth and sixth order precision arefirstly established,followed by an adoption of the Richardson extrapolation method to obtain the extrapolation schemes with sixth and eighth order precision on this basis.The established difference scheme can be verified by two Poisson equation examples.The numerical example results show that the adoption of the Richardson extrapolation method based on the compact difference scheme is able to obtain effective and robust high-precision numerical solutions.

关 键 词：计算数学 椭圆型偏微分方程 紧致差分格式 RICHARDSON外推法 高阶精度 

分 类 号：O242.2[理学—计算数学]