高阶抛物型方程的一族高精度恒稳差分格式  

A FAMILY OF ABSOLUTELY STABLE DIFFERENCE SCHEMES OF HIGH ACCURACY FOR SOLVING HIGH ORDER PARABALIC EQUATION

作　　者：曾文平[1] 

机构地区：[1]华侨大学数学系,泉州362011

出　　处：《计算数学》2003年第3期347-354,共8页Mathematica Numerica Sinica

摘　　要：本文考虑如下的高阶(2m阶)A family of three-layer implicit difference Schemes of high accuracy with two parameters for solving high order parabolic equation (where m is positive integers) are constructed. In the special case α =1/2、β= 0, We obtain a two-layer difference scheme. These schemes are proved to be absolutely stable for arbiratily chosen non-negative parameters, And the order of the truncation error is O((Δt)2 +(Δx)6). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.

关 键 词：抛物型方程 隐式差分格式 精度 周期初值问题 截断误差 稳定性 

分 类 号：O241.8[理学—计算数学]