一类偏微分方程边值问题的有限差分格式  

Finite Difference Scheme for a Class of Boundary Value Problems

作　　者：武文佳[1] 

机构地区：[1]上海电机学院数理教学部,上海201306

出　　处：《上海电机学院学报》2017年第1期56-62,共7页Journal of Shanghai Dianji University

基　　金：上海电机学院学科建设项目资助(16JCXK02)

摘　　要：对一类二维常系数椭圆型偏微分方程,建立了一种四阶紧有限差分格式。证明了有限差分解的存在性和唯一性,用离散能量分析的方法给出了数值解的L^2-范数和H^1-范数误差估计。A fourth-order compact finite difference scheme is proposed for a class of two-dimensional elliptic boundary value problems with the constant coefficients.Existence and uniqueness of finite difference solutions are investigated.Convergence and the fourth-order accuracy of the proposed method are shown with respect to discrete L^2-and H^1-norm.

关 键 词：常系数椭圆边值问题 紧有限差分格式 误差估计 

分 类 号：O241.82[理学—计算数学]