解二阶抛物型方程的一族高精度恒稳格式  

A Group of Steady Difference Schemes with High Accuracy for Solving Two-Order Parabolic Equation

作　　者：张星[1] 单双荣[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2009年第2期229-232,共4页Journal of Huaqiao University(Natural Science)

基　　金：国务院侨办科研基金资助项目(04QZR09)

摘　　要：对二阶抛物型方程构造了一族含参数高精度三层差分格式.当参数满足一定的条件时,差分格式绝对稳定,其局部截断误差阶数最高可达O(2τ+h4).适当地调节参数,可以得到一个七点显式差分格式和一个两层六点隐格式.数值例子表明,对稳定性所作的分析是正确的.A family of high-accurate and three-layer difference schemes containing parameters are constructed for solvingtwo-order parabolic equation. These difference schemes are stable when the parameters satisfy a certain condition. The local truncation error can reach the order of O（x^2 ＋h^4 ）. The analysis of stability is consistent as illustrated by numerical example.

关 键 词：二阶抛物型方程 差分格式 绝对稳定 截断误差 

分 类 号：O241.82[理学—计算数学]