一类双调和方程边值问题的四阶和六阶Richardson外推法  

The Fourth and Sixth-Order Richardson Extrapolation Method for a Class of Biharmonic Equation Boundary Value Problems

作　　者：刘凯 张海湘 杨雪花 石扬 LIU Kai;ZHANG Haixiang;YANG Xuehua;SHI Yang(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》2025年第2期78-86,共9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：首先,对双调和方程建立了具有二阶精度的差分格式,证明了该差分格式的解存在唯一性,并利用极值原理证明了其收敛性和稳定性;利用双重Richardson外推法对该差分格式做了一次外推和二次外推,在内结点处使得计算结果分别具有四阶精度和六阶精度。研究结果表明,外推算法在一定条件下对于提高差分格式解的精度有显著的作用。Firstly,a difference scheme with the second-order accuracy is established for the biharmonic equation,thus proving the uniqueness of the solution of this difference scheme,with the convergence and stability further demonstrated by using the extremum principle.The double Richardson extrapolation method is adopted to extrapolate the difference scheme with two sequential extrapolations,resulting in the fourth and the sixth order accuracy at the inner nodes,respectively.The research results indicate that the proposed extrapolation method exerts a significant effect on the improvement of the accuracy of differential scheme solutions under certain conditions.

关 键 词：计算数学 双调和方程 数值解 RICHARDSON外推法 收敛性 稳定性 

分 类 号：Q241.82[生物学—细胞生物学]