解四阶抛物型方程的两层高精度差分格式  

High-Accurate and Two-Layer Difference Schemes for Solving Four-Order Parabolic Equation

作　　者：崔晓鹏[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）》2011年第6期710-713,共4页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金(青年科学基金)资助项目(11001090)

摘　　要：对任意常数a>0的四阶抛物型方程,构造含参数的高精度两层差分格式.当参数满足一定的条件时,局部截断误差阶最高可达到O(τ2+h6),并且是绝对稳定的.特殊情况下,则为一个条件稳定的两层显格式.数值例子表明,稳定性分析是正确的.A family of high-accurate and two-layer difference schemes with parameters are constructed for solving fourorder parabolic equation with arbitrary constant coefficient a〉0. The local truncation error can reach the order of O（τ^2＋h^6）as the maximum when the parameters satisfy a certain condition and these difference schemes are absolutely stable. In special case, one-layer conditionally stable difference scheme is obtained. The analysis of stability is correct, as illustrated by numerical example.

关 键 词：四阶抛物型方程 差分格式 高精度 截断误差 稳定性 

分 类 号：O241.82[理学—计算数学]