求解三维热传导方程的高效精确算子分裂方法  

An efficient and accurate operating splitting method for solving 3D heat conduction equations

作　　者：武莉莉 WU Li-li(School of Mathematics and Statistics, Ningxia University, Yinchuan 750021,China;School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021 [2]宁夏师范学院数学与计算机科学学院,宁夏固原756000

出　　处：《兰州理工大学学报》2020年第5期166-172,共7页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11772165,11701306)。

摘　　要：提出了求解三维热传导方程的两种算子分裂局部一维格式.分别利用两种Padé格式逼近时间导数,以及两种高精度紧致格式用于计算空间导数.两种算子分裂局部一维格式的精度分别为四阶和六阶.通过矩阵分析理论严格证明了两种格式均是无条件稳定的.通过数值实验验证了所提格式的性能.The operator splitting local one-dimensional method is employed to resolve three-dimensional(3D)heat conduction equations.Two kinds of Padéapproximations are used to calculate the temporal derivative,and two kinds of high-order difference formulas are used to calculate the spatial derivatives.Then,two kinds of efficient splitting local one-dimensional schemes are derived.The accuracy of them are the fourth-and sixth-order,respectively.The unconditional stability of both methods is proved by the rigorous matrix analysis theory.Numerical examples are resolved to validate the performances of the present method.

关 键 词：热传导方程 算子分裂 局部一维格式 高精度 无条件稳定 

分 类 号：O241.82[理学—计算数学]