求解一维热传导方程的一族三层隐格式  

A Class of Three-Level Implicit Difference Scheme for Solving One-Dimensional Heat Conduction Parabolic Equations

作　　者：詹涌强 凌婷 ZHAN Yong-qiang;LING Ting(Department of Mathematics Teaching and Research, Guangdong Communication Polytechnic College, Guangzhou 510800, China)

机构地区：[1]广东交通职业技术学院基础部数学教研室,广州510800

出　　处：《西南师范大学学报（自然科学版）》2020年第11期1-5,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(61070165).

摘　　要：用待定系数法构造了求解一维热传导方程的一族高精度隐式格式.格式的截断误差达到O(τ3+h6).证明了当r<√5/10时,差分格式是稳定的.通过数值试验,比较了差分格式的解和精确解的区别,说明了差分格式的有效性.This paper presents a class of implicit difference schemes with high accuracy for solving one-dimension heat conduction equation by the method of undetermined parameters.The truncation error of the schemes is O(τ3+h6).The difference schemes are proved to be stable if r<√5/10.The numerical experiment shows the numerical solutions of difference schemes and the precise solutions are matched and the difference schemes are effective.

关 键 词：一维热传导方程 隐式差分格式 截断误差 

分 类 号：O241.82[理学—计算数学]