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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (4): 460-468    DOI: 10.3785/j.issn.1008-9497.2020.04.009
数学与计算机科学     
奇异摄动问题在修正的Bakhvalov-Shishkin网格上的混合差分格式
郑权1, 刘颖1, 刘忠礼2
1.北方工业大学 理学院，北京 100144
2.北京联合大学 生物化学工程学院，北京 100023
The hybrid finite difference schemes on the modified Bakhvalov-Shishkin mesh for the singularly perturbed problem
ZHENG Quan1, LIU Ying1, LIU Zhongli2
1.College of Sciences, North China University of Technology, Beijing 100144, China
2.College of Biochemical Engineering, Beijing Union University, Beijing 100023, China
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摘要： 在分3段修正的Bakhvalov-Shishkin网格上，将中点迎风格式和中心差分格式相结合，建立了新混合差分格式算法，以求解一维奇异摄动两点边值问题。借助截断误差、离散比较原理和障碍函数等，得到了与摄动参数ε一致的较好的收敛阶数，从粗网格部分到细网格部分依次为二阶收敛、一阶收敛和二阶收敛。数值算例表明，该方法在实际求解精度上较其他3种方法优越。
关键词： 奇异摄动两点边值问题;  新混合差分格式;  修正的Bakhvalov-Shishkin网格;  误差估计    
Abstract: This paper develops a new hybrid finite difference scheme combining the midpoint upwind scheme with the central difference scheme on a three-piece modified Bakhvalov-Shishkin mesh to solve the singularly perturbed two-point boundary value problem. Better ε-uniform accuracy and order of convergence are obtained by adopting truncation error, discrete comparison principle, barrier functions and so on. From the coarse mesh to the fine mesh, the error estimate of second-order convergence, first-order convergence and second-order convergence are obtained in turn. The numerical examples confirm the theoretical results and illustrate the advantage on accuracy of the method over the other three methods.
Key words: the modified Bakhvalov-Shishkin mesh    error estimate    new hybrid finite difference scheme    singularly perturbed two-point boundary value problem
收稿日期: 2018-06-27 出版日期: 2020-07-25
CLC:  O 241  
基金资助: 国家自然科学基金资助项目(11471019)；北京市自然科学基金资助项目 (1122014).
通讯作者: ORCID:http://orcid.org//0000-0002-7005-3680，E-mail：liuzhongli2@163.com.     E-mail: liuzhongli2@163.com
作者简介: 郑权(1964—)，ORCID:http://orcid.org//0000-0002-4859-9994，男，博士，教授，主要从事微分方程数值解法研究.。
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引用本文:

郑权, 刘颖, 刘忠礼. 奇异摄动问题在修正的Bakhvalov-Shishkin网格上的混合差分格式[J]. 浙江大学学报（理学版）, 2020, 47(4): 460-468.

ZHENG Quan, LIU Ying, LIU Zhongli. The hybrid finite difference schemes on the modified Bakhvalov-Shishkin mesh for the singularly perturbed problem. Journal of Zhejiang University (Science Edition), 2020, 47(4): 460-468.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.04.009    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I4/460

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