多维热传导方程的紧交替方向差分格式

数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 556-562.

多维热传导方程的紧交替方向差分格式

1. Department of Mathematics, Henan Institute of Science and Technology2. Department of Mathematics and Information Sciences, North China University of Water Conservancy and Electric Power

收稿日期:2009-03-31 出版日期:2011-12-30 发布日期:2023-04-14
作者简介:WANG Xiao-feng(1977-), male(Mongolian), native of Neixiang, Henan, Ph.D., engages in numerical solution of partial differential equations; YUAN He-cai(1978-), male, native of Lankao, Henan, a lecturer of North China University of Water Conservancy and Electric Power, M.S.D., engages in OR and analytic inequalities.
基金资助:
Supported by the NNSF of China(10971159)

Compact ADI Method for Solving Heat Equations in Multi-dimension

1. Department of Mathematics, Henan Institute of Science and Technology2. Department of Mathematics and Information Sciences, North China University of Water Conservancy and Electric Power

Received:2009-03-31 Online:2011-12-30 Published:2023-04-14
About author:WANG Xiao-feng(1977-), male(Mongolian), native of Neixiang, Henan, Ph.D., engages in numerical solution of partial differential equations; YUAN He-cai(1978-), male, native of Lankao, Henan, a lecturer of North China University of Water Conservancy and Electric Power, M.S.D., engages in OR and analytic inequalities.
Supported by:
Supported by the NNSF of China(10971159)

摘要/Abstract

摘要： A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ²+h⁴). It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ³+h⁶) is gained with once Richardson’s extrapolation. Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.

关键词: heat equation, differential operators, ADI difference scheme, absolutely stable

Abstract:

A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ²+h⁴). It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ³+h⁶) is gained with once Richardson’s extrapolation. Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.

Key words: heat equation, differential operators, ADI difference scheme, absolutely stable

中图分类号:

O241.82

王晓峰, 袁合才. 多维热传导方程的紧交替方向差分格式[J]. 数学季刊, 2011, 26(4): 556-562.

WANG Xiao-feng, YUAN He-cai. Compact ADI Method for Solving Heat Equations in Multi-dimension[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(4): 556-562.

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