二阶椭圆型偏微分方程有限分析解法的精度研究  

The Accuracy Research for the Finite Analytic Method of Ellipse-type Differential Equations

作　　者：李东波[1] 臧国才[1] 

机构地区：[1]南京理工大学制造系,南京理工大学动力工程学院

出　　处：《南京理工大学学报》1996年第1期83-86,共4页Journal of Nanjing University of Science and Technology

摘　　要：该文对单元内二阶椭圆型偏微方程有限分析解法的精度作了深入研究。首先应用有限分析方法对求得单元内二阶椭圆型方程的有限分析解，其后通过泰勒级数展开方法，对单元内二阶椭圆型偏微分方程的有限分析解作了展开，引入算子将复杂方程进一步简化，证明了在任意边界近似函数条件下单元内二阶椭圆型偏微分方程的有限分析解的精度为步长ｈ的Ｏ（ｈ４）。结果为有限分析法解工程椭圆型偏微分方程问题，在解法精度上提供了保障。his paper concentrates effort on the accuracy of the finite analyticnumerical solution for ellipse-type differential equations.The FA method is applied to get the finite analytic solution of ellipse partial differential equations in a typical element.Then by Tailor progression expansion method,the finite analytic solution for two dimision ellipse-type differential equation in the typical element is expanded.By introducing mathematics-operator the complex question is simplified and the finite analytic solution in any boundary approximate function is proved to have an accuracy of b(h4).The result is very meaningful for the accuracy of the finite analytic numerical solution for ellipse-type partial differential equations.

关 键 词：分析解法 精度 偏微分方程 椭圆型方程 

分 类 号：O175.25[理学—数学]