求解三维热传导方程的高效精确算子分裂方法

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (5): 166-172.

• 数理科学 • 上一篇

求解三维热传导方程的高效精确算子分裂方法

武莉莉^1,2

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

收稿日期:2020-05-20 出版日期:2020-10-28 发布日期:2020-11-06
作者简介:武莉莉(1980-),女,宁夏西吉人,博士生,副教授.
基金资助:
国家自然科学基金(11772165,11701306)

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

WU Li-li^1,2

1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021,China;
2. School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China

Received:2020-05-20 Online:2020-10-28 Published:2020-11-06

摘要/Abstract

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.

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

Abstract: The operator splitting local one-dimensional method is employed to resolve three-dimensional (3D) heat conduction equations. Two kinds of Padé approximations 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.

Key words: heat conduction equation, operator splitting, local one-dimensional scheme, high accuracy, unconditional stability

中图分类号:

O241.82

武莉莉. 求解三维热传导方程的高效精确算子分裂方法[J]. 兰州理工大学学报, 2020, 46(5): 166-172.

WU Li-li. An efficient and accurate operating splitting method for solving 3D heat conduction equations[J]. Journal of Lanzhou University of Technology, 2020, 46(5): 166-172.

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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

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