[1]滕宇航,赖艺颖,黄浪扬.应用重心插值的Burgers方程数值解法[J].华侨大学学报(自然科学版),2025,(1):104-112.[doi:10.11830/ISSN.1000-5013.202311015]
　TENG Yuhang,LAI Yiying,HUANG Langyang.Numerical Solution Method of Burgers Equation Using Barycentric Interpolation[J].Journal of Huaqiao University(Natural Science),2025,(1):104-112.[doi:10.11830/ISSN.1000-5013.202311015]
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应用重心插值的Burgers方程数值解法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
期数:
2025年第1期
页码:
104-112
栏目:
出版日期:
2025-01-10

文章信息/Info

Title:
Numerical Solution Method of Burgers Equation Using Barycentric Interpolation
文章编号:
1000-5013(2025)01-0104-09
作者:
滕宇航;  赖艺颖;  黄浪扬
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
TENG Yuhang;  LAI Yiying;  HUANG Langyang
School of Mathematical Science, Huaqiao University, Quanzhou 362021, China
关键词:
Burgers方程;  重心插值配点法;  Crank-Nicolson差分法;  相容性分析
Keywords:
Burgers equation;  barycentric interpolation collocation method;  Crank-Nicolson difference method;  compatibility analysis
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202311015
文献标志码:
A
摘要:
利用重心插值构造求解Burgers方程的无网格数值方法。在时间方向用Crank-Nicolson差分法对方程进行离散,在空间方向用重心插值切比雪夫配点法逼近函数本身及其空间导数。 对全离散数值格式进行相容性分析。数值算例表明:与经典的有限差分方法比较,重心插值配点法用较少的节点就能达到较高的精度。
Abstract:
The meshless numerical method of Burgers equation is solved using barycentric interpolation construction. The equation is discretized using the Crank-Nicolson difference method in the time direction. The function is approximated to itself and so is its spatial derivative using barycentric interpolation Chebyshev collocation method in spatial direction. The compatibility analysis of the fully discrete numerical value scheme is perfomed. Numerical experiments show that, compared with the classical finite difference method, the barycentric interpolation collocation method can achieve higher accuracy with fewer nodes.

参考文献/References:

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相似文献/References:

[1]翁智峰,姚泽丰,赖淑琴.重心插值配点法求解Allen-Cahn方程[J].华侨大学学报(自然科学版),2019,40(1):133.[doi:10.11830/ISSN.1000-5013.201806043]
　WENG Zhifeng,YAO Zefeng,LAI Shuqin.Barycentric Interpolation Collocation Method for Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2019,40(1):133.[doi:10.11830/ISSN.1000-5013.201806043]
[2]邓杨芳,姚泽丰,汪精英,等.二维Allen-Cahn方程的有限差分法/配点法求解[J].华侨大学学报(自然科学版),2020,41(5):690.[doi:10.11830/ISSN.1000-5013.202001001]
　DENG Yangfang,YAO Zefeng,WANG Jingying,et al.Two Dimensional Allen-Cahn Equation Solved By FiniteDifference Method/Collocation Method[J].Journal of Huaqiao University(Natural Science),2020,41(1):690.[doi:10.11830/ISSN.1000-5013.202001001]
[3]黄蓉,翁智峰.时间分数阶Allen-Cahn方程的重心插值配点法[J].华侨大学学报(自然科学版),2022,43(4):553.[doi:10.11830/ISSN.1000-5013.202104060]
　HUANG Rong,WENG Zhifeng.Barycentric Interpolation Collocation Method for Time-Fractional Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2022,43(1):553.[doi:10.11830/ISSN.1000-5013.202104060]

备注/Memo

备注/Memo:
收稿日期: 2023-11-03
通信作者: 黄浪扬(1976-),男,副教授,主要从事偏微分方程保结构算法的研究。E-mail:hly6@163.com。
基金项目: 国家自然科学基金资助项目(11701197); 福建省自然科学基金面上资助项目(2022J01308); 中央高校基本科研业务费专项基金资助项目(ZQN702)
更新日期/Last Update: 2025-01-20