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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 (3): 397-410.doi: 10.3969/j.issn.1005-3085.2025.03.001doi: 32411.14.1005-3085.2025.03.001

• •    下一篇

三维扩散方程的一类逐次置换迭代方法

潘云鸣,  许秋燕   

  1. 宁夏大学数学统计学院，银川 750021
  • 收稿日期:2022-10-07 接受日期:2023-03-29 出版日期:2025-06-15 发布日期:2025-06-15
  • 通讯作者: 许秋燕 E-mail: qiuyanxu@nxu.edu.cn
  • 基金资助:
    国家自然科学基金 (12202219; 12061057)；宁夏自然科学基金 (2024AAC02009)；宁夏大学研究生创新计划 (CXXM2022-10).

A Class of Successive Permutation Iterative Algorithms for Three-dimensional Diffusion Equation

PAN Yunming,  XU Qiuyan   

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021
  • Received:2022-10-07 Accepted:2023-03-29 Online:2025-06-15 Published:2025-06-15
  • Contact: Q. Xu. E-mail address: qiuyanxu@nxu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12202219; 12061057); the Natural Science Foundations of Ningxia (2024AAC02009); the Graduate Innovation Program of Ningxia University (CXXM2022-10).

摘要：

在全隐式离散的基础上，构造了一类求解三维扩散方程的逐次置换迭代方法。给出了方法的增长矩阵，并对其稳定性进行了分析。新方法避免了求解大型线性方程组的困难，从而显著地提高了计算速度。与全隐式差分法和Gauss-Seidel迭代法比较，新方法不仅与全隐式差分法具有同样的精度，而且比Gauss-Seidel迭代法更快更精确。

关键词: 扩散方程, 全隐式格式, 逐次置换迭代, 增长矩阵, 收敛性

Abstract:

In this paper, a class of successive permutation iterative methods for solving three-dimensional diffusion equations is constructed based on full-implicit discretization. The growth matrix of the method is given in this paper, and the convergence is analyzed. The new method can avoid solving large linear equations, and thus significantly improve the calculation speed. Compared with the full-implicit method and the Gauss-Seidel method, the new method not only has the same approximate accuracy as the full-implicit method but also is faster and more accurate than the Gauss-Seidel method.

Key words: diffusion equation, full-implicit scheme, successive placement iteration, growth matrix, convergence

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