[1]李冉冉,王红玉,开依沙尔·热合曼*.求解对流扩散方程的4阶紧致差分格式[J].江西师范大学学报(自然科学版),2022,(05):517-522.[doi:10.16357/j.cnki.issn1000-5862.2022.05.12]
　LI Ranran,WANG Hongyu,KAYSAR Rahman*.The Fourth-Order Compact Finite Difference Scheme for the Convection Diffusion Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2022,(05):517-522.[doi:10.16357/j.cnki.issn1000-5862.2022.05.12]
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求解对流扩散方程的4阶紧致差分格式()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年05期
页码:
517-522
栏目:
数学与应用数学
出版日期:
2022-09-25

文章信息/Info

Title:
The Fourth-Order Compact Finite Difference Scheme for the Convection Diffusion Equation
文章编号:
1000-5862(2022)05-0517-06
作者:
李冉冉; 王红玉; 开依沙尔·热合曼*
(新疆大学数学与系统科学学院,新疆 乌鲁木齐 830046)
Author(s):
LI Ranran; WANG Hongyu; KAYSAR Rahman*
(College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China)
关键词:
对流扩散方程;  紧致差分格式;  Hermite插值;  Dirichlet边界条件
Keywords:
convection diffusion equation;  high-order compact finite difference;  Hermite formula;  Dirichlet boundary conditions
分类号:
O 211.67
DOI:
10.16357/j.cnki.issn1000-5862.2022.05.12
文献标志码:
A
摘要:
该文提出了在周期和Dirichlet边界条件下的1维对流扩散方程的紧致差分格式.在这2种边界条件下对空间变量使用4阶紧致差分格式,对时间变量利用3次Hermite插值公式构造空间和时间同时具有4阶精度的数值格式,并证明了格式的绝对稳定性,最后通过对2种边界条件下的算例进行数值实验和比较,验证了格式的精确性和可靠性.
Abstract:
In this paper,a compact difference scheme for the one-dimensional convection diffusion equation under periodic and Dirichlet boundary conditions is proposed.The fourth-order compact difference scheme is used for the spatial variables under these two boundary conditions,and the numerical scheme with both spatial and temporal fourth-order accuracy is constructed using the cubic Hermite interpolation formula for the temporal variables.Finally,the accuracy and reliability of the scheme is verified by numerical experiments and comparisons of numerical examples under two boundary conditions.

参考文献/References:

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相似文献/References:

[1]开依沙尔·热合曼,努尔买买提·黑力力.求解对流扩散方程的Pade'逼近格式[J].江西师范大学学报(自然科学版),2014,(03):261.
　KAYSAR Rahman,NURMAMAT Helil.The Pade' Approximation Scheme for Solving Convection-Diffusion Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(05):261.

备注/Memo

备注/Memo:
收稿日期:2022-05-12
基金项目:国家自然科学基金(11461069)和新疆大学博士启动基金(BS150204)资助项目.
通信作者:开依沙尔·热合曼(1978—),男,新疆库车人,副教授,博士,主要从事微分方程数值计算方面的研究.E-mail:kaysar2014@sina.com
更新日期/Last Update: 2022-09-25