求解扩散方程的高精度显式紧致差分格式

doi:10.3969/j.issn.1000-1565.2016.02.002

河北大学学报(自然科学版) ›› 2016, Vol. 36 ›› Issue (2): 117-123.DOI: 10.3969/j.issn.1000-1565.2016.02.002

求解扩散方程的高精度显式紧致差分格式

杨晓佳,王燕

收稿日期:2015-09-08 出版日期:2016-03-25 发布日期:2016-03-25
通讯作者: 王燕(1976—),女,宁夏银川人,宁夏大学副教授,主要从事偏微分方程数值解法的研究.E-mail:wangy@nxu.edu.cn
作者简介:杨晓佳(1988—),女,宁夏吴忠人,宁夏大学在读硕士研究生. E-mail:yang_xiaoj@sina.com 〓通信作者:王燕(1976—),女,宁夏银川人,宁夏大学副教授,主要从事偏微分方程数值解法的研究. E-mail:wangy@nxu.edu.cn
基金资助:
宁夏高等学校科学技术研究项目(NGY2013019)

High accuracy explicit compact difference scheme for the diffusion equation

YANG Xiaojia,WANG Yan

College of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received:2015-09-08 Online:2016-03-25 Published:2016-03-25

摘要/Abstract

摘要： 首先针对一维扩散方程,空间方向采用二阶导数的四阶紧致差分公式进行离散,时间方向采用泰勒级数展开的方法进行离散,推导出了一种高精度显式紧致差分格式;然后通过Fourier分析方法给出了格式的稳定性条件为λ≤1/2(λ为网格比);最后通过数值实验验证了格式的精确性和可靠性.

关键词: 扩散方程, 高精度, 紧致格式, 显格式, 有限差分法

Abstract: Based on the fourth-order compact difference formula of the second-order derivative in spatial direction and Taylor series expansion in time direction,a high-order explicit compact difference scheme for the one dimentional diffusion equation is developed.The stability of the scheme is analyzed by Fourier method,and the condition of stability is λ≤1/2(λ is the mesh ratio).Numerical experiments are carried out to verify the accuracy and reliability of the present scheme.

Key words: diffusion equation, high accuracy, compact scheme, explicit scheme, finite difference method

中图分类号:

O241.82

杨晓佳,王燕. 求解扩散方程的高精度显式紧致差分格式[J]. 河北大学学报(自然科学版), 2016, 36(2): 117-123.

YANG Xiaojia,WANG Yan. High accuracy explicit compact difference scheme for the diffusion equation[J]. Journal of Hebei University (Natural Science Edition), 2016, 36(2): 117-123.

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求解扩散方程的高精度显式紧致差分格式

High accuracy explicit compact difference scheme for the diffusion equation

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