全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
计算数学  2015 

广义sine-Gordon方程高精度隐式紧致差分方法

, PP. 199-212

Keywords: SG方程,紧致差分格式,交替方向隐格式,外推法,能量分析法

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.

References

[1]  Scott A C. Propagation of Magnetic Flux on a long Josephson Tunnel Junction[J]. Il Nuovo Cimento B, 1970, B69: 241-252.
[2]  Ghidaglia J M and Temam R. Attractors for damped nonlinear hyperbolic equations[J]. Journal de Mathematiques Pures et Appliquees, 1987, 66: 273-319.
[3]  向正, 彭志雄, 王明亮. Sinh-gordon方程的一种解法[J]. 河南科技大学 学报(自然科学版), 2004, 25(2): 87-90.
[4]  Hu H C and Lou S Y. New quasi-periodic waves of the (2+1)-dimensional sine-Gordon system[J]. Physics Letters A, 2005, 341: 422-426.
[5]  方樾, 马小龙. 一个非线性Sine-Gordon方程的一个蛙跳有限差分格 式[J]. 广西民族学院学报, 1996, 2(2): 17-21.
[6]  Bratsos A G and Twizell E H. The solution of the sine-Gordon equation using the method of lines[J]. International Journal of Computer Mathematics, 1996, 61: 271-292.
[7]  Bratsos A G and Twizell E H. A family of parametric finite-difference methods for the solution of the sine-Gordon equation[J], Applied Mathematics and Computation, 1998, 93: 117-137.
[8]  Bratsos A G. An explicit numerical scheme for the sine-Gordon equation in 2+1 dimensions[J]. Applied Numerical Analysis and Computational Mathematics, 2005, 2: 189-211.
[9]  Bratsos A G. A numerical method for the one-dimensional sine-Gordon equation[J]. Numerical Methods for Partial Differential Equations, 2008, 24: 833-844.
[10]  Bratsos A G. A fourth order numerical scheme for the one-dimensional sine-Gordon equation[J]. International Journal of Computer Mathematics, 2008, 85: 1083-1095.
[11]  许秋滨, 常谦顺. 广义非线性Sine-Gordon方程的两个隐式差分格式[J]. 应用数学学报, 2007, 30(2): 263-271.
[12]  胡劲松, 王玉兰. 广义非线性Sine-Gordon方程的一个隐式差分格式及其Richardson外推[J]. 西华大学学报, 2011, 30(4): 25-27.
[13]  周艳祖, 张义, 王潇, 黄国英, 张传林. 非线性Sine-Gordon方程的三种差分格式[J]. 暨南大学学报(自然科学版), 2008, 29(3): 233-238.
[14]  Mohebbi M and Dehghan M. High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods[J]. Mathematical and Computer Modelling, 2010, 51: 537-549.
[15]  Cui M. High order compact alternating direction implicit method for the generalized sine-Gordon equation[J]. Journal of Computional and Applied Mathematics, 2010, 235: 837-849.
[16]  Sari M and Gurarslan G. A sixth-order compact finite difference method for the one-dimensional sine-Gordon equation[J]. International Journal for Numerical Methods Biomedical Engineering, 2011, 27: 1126-1138.
[17]  刘洋, 李宏. 阻尼sine-Gordon方程的H1-Galerkin混合元方法数值解 [J]. 应用数学, 2009, 22(3): 579-588.
[18]  孙志忠. 偏微分方程的数值解法 [M]. 北京: 科学出版社, 2005.
[19]  孙志忠, 李雪玲. 反应扩散方程的紧交替方向差分格式 [J]. 计算数学, 2005, 27(2): 209-224. 浏览
[20]  Gao Z and Xie S. Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schr?dinger equations[J]. Applied Numerical Mathematics, 2011, 61: 593-614.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133