解高维热传导方程的一族高精度显式差分格式

数学季刊 ›› 2010, Vol. 25 ›› Issue (2): 236-243.

解高维热传导方程的一族高精度显式差分格式

1. Department of Mathematics, Xinxiang University2. Department of Basic Course, Jiaozuo University

收稿日期:2008-01-09 出版日期:2010-06-30 发布日期:2023-06-05
作者简介:CHEN Zhen-zhong(1957-), male, native of Huixian, Henan, a professor of Xinxiang University, engages in numerical solution of partial differential equations; MA Xiao-xia(1969-), female, native of Xiuwu,Henan, a lecturer of Jiaozuo University, M.S.D, engages in numerical solution of partial differential equations.
基金资助:
Supported by NSF of the Education Department of Henan Province(20031100010)；

A Class of High Accuracy Explicit Difference Schemes for Solving the Heat-conduction Equation of High-dimension

1. Department of Mathematics, Xinxiang University2. Department of Basic Course, Jiaozuo University

Received:2008-01-09 Online:2010-06-30 Published:2023-06-05
About author:CHEN Zhen-zhong(1957-), male, native of Huixian, Henan, a professor of Xinxiang University, engages in numerical solution of partial differential equations; MA Xiao-xia(1969-), female, native of Xiuwu,Henan, a lecturer of Jiaozuo University, M.S.D, engages in numerical solution of partial differential equations.
Supported by:
Supported by NSF of the Education Department of Henan Province(20031100010)；

摘要/Abstract

摘要： In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied. the truncation error reaches O(τ²+h⁴), and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.

关键词: heat-conduction equation, explicit difference scheme, truncation error, conditional stability

Abstract: In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied. the truncation error reaches O(τ²+h⁴), and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.

Key words: heat-conduction equation, explicit difference scheme, truncation error, conditional stability

中图分类号:

O241.82

陈贞忠, 马小霞. 解高维热传导方程的一族高精度显式差分格式[J]. 数学季刊, 2010, 25(2): 236-243.

CHEN Zhen-zhong, MA Xiao-xia. A Class of High Accuracy Explicit Difference Schemes for Solving the Heat-conduction Equation of High-dimension[J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 236-243.

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