解抛物型方程的九点隐格式  

The Implicit Differencing Scheme of Nine Points For Solving The Parabolic Equations

作　　者：曹俊英[1] 张大凯[1] 

机构地区：[1]贵州大学理学院数学系,贵州贵阳550025

出　　处：《贵州大学学报（自然科学版）》2006年第2期127-133,共7页Journal of Guizhou University:Natural Sciences

摘　　要：作者用组合差商的方法对一维抛物型方程构造了一类高精度的三层含参数隐式差分格式,格式的截断误差达到O(3τ+h6),绝对稳定.当参数取特定值时,格式的截断误差可以提高到O(4τ+h8),稳定性条件是0<r<120.当r取特定值时,格式的截断误差可达到O(τ5+h10).One class high accuracy implicit differencing schemes of three layers and nine points for solving the parabolic equations of one-dimensions is presented in this paper, the class of scheme uses combinatorial difference quotient method. It is an explicit scheme which has parameter, its truncation error is O （τ^3＋h^6） ,and the stability condition is absolute stability. When the parameter takes the special definite value, its truncation error is O（τ^4＋h^8）, the stability condition of which is r〈1/√20 when r takes the special definite value, its truncation error is O（τ^5＋h^10）.

关 键 词：一维抛物型方程 组合差商法 隐式差分格式 截断误差 稳定性条件 

分 类 号：O241.82[理学—计算数学]