求解二阶双曲型方程的自适应网格方法

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 942-950.

求解二阶双曲型方程的自适应网格方法

周琴^1,*(),杨银²

¹ 湖南涉外经济学院信息与机电工程学院长沙 410205
² 湘潭大学科学工程计算与数值仿真湖南省重点实验室湖南湘潭 411105

收稿日期:2018-04-02 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 周琴 E-mail:19891881@qq.com
基金资助:
国家自然科学基金(11671342);湖南省教育厅科学研究项目基金(18C1097);湖南省自然科学基金(2018JJ2374)

Adaptive Mesh Method for Solving a Second-Order Hyperbolic Equation

Qin Zhou^1,*(),Yin Yang²

¹ School of Information Mechanical and Electrical Engineering, Hunan International Economics University, Changsha 410205
² Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan Xiangtan 411105

Received:2018-04-02 Online:2019-08-26 Published:2019-09-11
Contact: Qin Zhou E-mail:19891881@qq.com
Supported by:
the NSFC(11671342);the Scientific Research Fund of Hunan Provincial Education Department(18C1097);the Natural Science Foundation of Hunan Province(2018JJ2374)

摘要/Abstract

摘要：

该文针对一类带小参数的二阶双曲型方程，提出了基于有限差分格式的自适应移动网格方法，给出了具体的移动网格算法，并通过数值实验验证了该方法的优越性，改进了均匀网格上求解的结果.

关键词: 双曲方程, 差分格式, 自适应移动网格, 网格迭代

Abstract:

In this paper, we study a class of second-order hyperbolic equations with small parameters. An adaptive moving mesh method for solving the equation with finite differencing scheme is proposed, and the moving mesh algorithm is given. The superiority of the method is verified by numerical experiments, and the result on uniform mesh is improved.

Key words: Hyperbolic equation, Difference scheme, Adaptive moving mesh, Mesh iteration

中图分类号:

O241.82

周琴,杨银. 求解二阶双曲型方程的自适应网格方法[J]. 数学物理学报, 2019, 39(4): 942-950.

Qin Zhou,Yin Yang. Adaptive Mesh Method for Solving a Second-Order Hyperbolic Equation[J]. Acta mathematica scientia,Series A, 2019, 39(4): 942-950.

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参考文献 13

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$N\times M$	$t=0.5$	$ r$	$ t=1$	$ r$	$ t=1.5$	$ r$	$ t=2$	$ r$
$50\times50$	9.508E-05		2.797E-04		5.684E-04		9.174E-04
$100\times100$	2.530E-05	1.91	8.225E-05	1.77	1.684E-04	1.76	2.673E-04	1.78
$200\times200$	8.934E-06	1.50	2.225E-05	1.89	4.630E-05	1.86	7.321E-05	1.87

$N\times M$	$t=0.5$	$r$	$ t=1$	$ r$	$t=1.5$	$ r$	$t=2$	$r$
$50\times50$	1.952E-04		7.678E-04		1.480E-03		2.196E-03
$100\times100$	5.472E-05	1.83	2.433E-04	1.66	4.720E-04	1.65	6.970E-04	1.66
$200\times200$	2.099E-05	1.38	6.838E-05	1.83	1.354E-04	1.80	1.999E-04	1.80

$N\times M$	$t=0.5$	$t=1$	$ t=1.5$	$ t=2$
$50\times50$	7.683E-04	2.571E-03	4.787E-03	6.949E-03
$100\times100$	3.513E-04	1.113E-03	1.902E-03	2.499E-03
$200\times200$	1.127E-04	3.276E-04	5.221E-04	6.652E-04

$N\times M$	$t=0.5$	$t=1$	$ t=1.5$	$t=2$
$50\times50$	5.433E-03	1.813E-02	3.353E-02	4.808E-02
$100\times100$	3.256E-03	1.001E-02	1.596E-02	1.834E-02
$200\times200$	1.201E-03	2.842E-03	4.560E-03	5.417E-03

$N\times M$	$t=0.5$	$r$	$t=1$	$r$	$ t=1.5$	$ r$	$ t=2$	$r$
$50\times50$	1.622E-04		2.400E-04		4.571E-04		6.861E-04
$100\times100$	4.274E-05	1.92	5.581E-05	2.10	1.147E-04	1.99	1.750E-04	1.97
$200\times200$	1.948E-05	1.13	1.698E-05	1.72	2.800E-05	2.03	4.703E-05	1.90