湖南工业大学学报2024，Vol.38Issue(1)：91-97,104,8.DOI:10.3969/j.issn.1673-9833.2024.01.013
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
摘要
Abstract
In view of the calculation of elliptic partial differential equations,compact difference schemes with fourth and sixth order precision are firstly 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Key words
computational mathematics/elliptic partial differential equation/compact difference scheme/Richardson extrapolation/high order accuracy分类
数理科学引用本文复制引用
李曹杰,张海湘,杨雪花..一类椭圆型Dirichlet边值问题的高精度Richardson外推法[J].湖南工业大学学报,2024,38(1):91-97,104,8.基金项目
国家自然科学基金资助项目(12226340,12226337,12126321) （12226340,12226337,12126321）
湖南省自然科学基金资助项目(2022JJ50083) （2022JJ50083）
湖南省教育厅优秀青年基金资助项目(21B0550) （21B0550）
