[1]盛华山.数值求解二维Sine-Gordon方程的C0P1时间递进方法[J].南京师范大学学报(自然科学版),2017,40(01):1.[doi:10.3969/j.issn.1001-4616.2017.01.001]
　Sheng Huashan.A C0P1 Time Stepping Method for Solving 2D Sine-Gordon Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(01):1.[doi:10.3969/j.issn.1001-4616.2017.01.001]
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数值求解二维Sine-Gordon方程的C0P1时间递进方法()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年01期
页码:
1
栏目:
·数学与计算机科学·
出版日期:
2017-03-31

文章信息/Info

Title:
A C0P1 Time Stepping Method for Solving 2D Sine-Gordon Equations
文章编号:
1001-4616(2017)01-0001-05
作者:
盛华山
上海交通大学数学科学学院,上海 200240
Author(s):
Sheng Huashan
School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China
关键词:
时间递进方法; sine-Gordon方程; 线性化插值; 全离散格式
Keywords:
time stepping method; sine-Gordon equations; linear interpolation; full-discrete scheme
分类号:
O24
DOI:
10.3969/j.issn.1001-4616.2017.01.001
文献标志码:
A
摘要:
提出了基于局部线性化的连续分片线性(以下简称C0P1)时间递进方法[1]求解二维sine-Gordon方程的数值方法. 首先在时间方向采用连续分片线性有限元离散,通过对sine-Gordon方程中各项分别采用显式或隐式线性化插值,导出时间半离散格式. 再在空间方向利用有限元方法[2]离散得到全离散格式. 若干数值试验证明了该方法的有效性.
Abstract:
This paper proposes a continuous piecewise linear(called C0P1 for short)time stepping method[1] combined with local linearization for solving 2D sine-Gordon equations. First of all,the sine-Gordon equations are discretized in time direction by a linear continuous Galerkin method combined with the explicit or implicit local linearization,leading to a semi-discrete scheme. Furthermore,a full-discrete scheme is obtained by spatial discretization with the finite element method[2]. Several numerical experiments are given to perform the effectiveness of the method.

参考文献/References:

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[7]GUO B,PASCUAL P,RODRIGUEZ M,et al. Numerical solution of the sine-Gordon equation[J]. Appl Math Comput,1986,18:1-14.
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备注/Memo

备注/Memo:
收稿日期:2016-09-18.
基金项目:国家自然科学基金面上项目(11571237).
通讯联系人:盛华山,博士生,研究方向:科学计算. E-mail:shs3701001@sjtu.edu.cn
更新日期/Last Update: 1900-01-01