一维非定常对流扩散反应方程的高精度紧致差分格式

doi:10.3969/j.issn.1000-1565.2017.01.002

河北大学学报(自然科学版) ›› 2017, Vol. 37 ›› Issue (1): 5-12.DOI: 10.3969/j.issn.1000-1565.2017.01.002

一维非定常对流扩散反应方程的高精度紧致差分格式

杨晓佳,田芳

收稿日期:2016-03-28 出版日期:2017-01-25 发布日期:2017-01-25
通讯作者: 田芳(1979—),女,宁夏中宁人,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:tianfsunny@126.com
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
基金资助:
国家自然科学基金资助项目(11361045;11161036);宁夏大学自然科学基金项目资助(ZR15014);宁夏大学研究生创新项目(GIP201620)

High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation

YANG Xiaojia,TIAN Fang

School of Mathematics and Statistis Science, Ningxia University, Yinchuan 750021, China

Received:2016-03-28 Online:2017-01-25 Published:2017-01-25

摘要/Abstract

摘要： 针对一维非定常对流扩散反应方程,首先推导了一种新的2层高精度紧致差分隐格式,其截断误差为O(τ²+τh²+h⁴),即当τ=O(h²)时,格式空间具有四阶精度;然后采用Fourier分析方法分析了格式的稳定性;最后通过数值算例验证了本文格式的精确性和可靠性.

关键词: 对流扩散反应方程, 非定常, 紧致差分格式, 隐式格式, 高精度

Abstract: A two-level high order compact finite difference implicit scheme is proposed to solve the one-dimensional unsteady convection diffusion reaction equation.The local truncation error of the scheme is O(τ²+τh²+h⁴),i.e.the scheme is the fourth order accuracy for space when τ=O(h²).Then,Fourier analysis method is used to prove the stability of the scheme.Finally,numerical experiments are conducted to verify the accuracy and the reliability of the present scheme.

Key words: convection diffusion reaction equation, unsteady, compact difference scheme, implicit scheme, high accuracy

中图分类号:

O241.82

杨晓佳,田芳. 一维非定常对流扩散反应方程的高精度紧致差分格式[J]. 河北大学学报(自然科学版), 2017, 37(1): 5-12.

YANG Xiaojia,TIAN Fang. High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(1): 5-12.

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一维非定常对流扩散反应方程的高精度紧致差分格式

High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation

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