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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (1): 13-31.doi: 10.3969/j.issn.1005-3085.2025.01.002

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对流扩散反应方程的六阶混合型紧致差分格式

王明镜,  田  芳   

  1. 宁夏大学数学统计学院，银川 750021
  • 收稿日期:2022-07-11 接受日期:2023-04-06 出版日期:2025-02-15 发布日期:2025-04-15
  • 通讯作者: 田芳 E-mail: tianfsunny@126.com
  • 基金资助:
    国家自然科学基金(11902170)；宁夏自然科学基金(2020AAC03059)；2024年自治区重点研发计划引才专项(2024YCZX0106).

Six Order Mixed Compact Difference Schemes for Convection Diffusion Reaction Equations

WANG Mingjing,  TIAN Fang   

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021
  • Received:2022-07-11 Accepted:2023-04-06 Online:2025-02-15 Published:2025-04-15
  • Contact: F. Tian. E-mail address: tianfsunny@126.com
  • Supported by:
    The National Natural Science Foundation of China (11902170); the Natural Science Foundation of Ningxia (2020AAC03059); the Key Research and Development Program of the Autonomous Region in 2024 (Special Projects for Talent Introduction) (2024YCZX0106).

摘要：

针对变系数对流扩散反应方程，构造了三种六阶混合型紧致差分格式。首先，基于泰勒级数展开推导了高阶导数的高阶差分逼近算子。然后，采用截断误差余项修正法，利用原模型方程，得到了求解对流扩散反应方程的三种六阶混合型紧致差分格式。最后，选取典型算例进行了数值实验，验证了所提格式的精度。

关键词: 对流扩散反应方程, 紧致差分格式, 高精度

Abstract:

For the variable coefficient convection-diffusion reaction equation, three sixth-order hybrid compact difference schemes are constructed. Firstly, the high-order difference approximation operator of high-order derivatives is derived based on Taylor series expansion. Then, by using the truncation error residual correction method and the original model equation, three sixth-order hybrid compact difference schemes for solving the convection-diffusion reaction equation are obtained. Finally, typical numerical examples are selected to conduct numerical experiments to verify the accuracy of the proposed schemes.

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

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