[1]吴龙渊,汪精英,翟术英.求解二维Allen-Cahn方程的两种ADI格式[J].华侨大学学报(自然科学版),2019,40(3):412-420.[doi:10.11830/ISSN.1000-5013.201810014]
　WU Longyuan,WANG Jingying,ZHAI Shuying.Two ADI Schemes for Solving Two-Dimensional Alleb-Cahn Equations[J].Journal of Huaqiao University(Natural Science),2019,40(3):412-420.[doi:10.11830/ISSN.1000-5013.201810014]
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求解二维Allen-Cahn方程的两种ADI格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第40卷
期数:
2019年第3期
页码:
412-420
栏目:
出版日期:
2019-05-20

文章信息/Info

Title:
Two ADI Schemes for Solving Two-Dimensional Alleb-Cahn Equations
文章编号:
1000-5013(2019)03-0412-09
作者:
吴龙渊;  汪精英;  翟术英
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WU Longyuan;  WANG Jingying;  ZHAI Shuying
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Allen-Cahn方程;  算子分裂;  交替方向隐格式;  傅里叶分析;  极大值原理
Keywords:
Allen-Cahn equation;  operator split;  alternating direction implicitscheme;  Fourier analysis;  maximum principle
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.201810014
文献标志码:
A
摘要:
为了构建二维Allen-Cahn方程的高效数值格式,利用算子分裂方法将原方程离散成非线性方程和二维热传导方程,其中,非线性方程有解析解.二维热传导方程时间离散采用Crank-Nicolson格式,空间离散分别采用二阶中心差分和四阶Padé逼近,得到两个稳定的数值格式.数值实验结果表明:格式具有有效性;能量呈现递减规律.
Abstract:
Construct an efficient numerical scheme for the two-dimensional Allen-Cahn equation. The original equation is discretized into a nonlinear equation and a two-dimensional heat conduction equation by using the operator splitting method in which the nonlinear equation has an analytical solution. To the two-dimensional heat conduction equation, the time dispersion is in the Crank-Nicholson scheme, and the spatial discretization is obtained by using the second-order center difference and the fourth-order Padé approximation respectively, we two stable numerical schemes. Numerical experiments demonstrate the validity of the schemes and the law of energy diminution.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2018-10-27
通信作者: 翟术英(1986-),女,副教授,博士,主要从事高阶差分格式的构造、分数阶高效数值算法的研究.E-mail:zhaishuying123456@163.com.
基金项目: 国家自然科学基金资助项目(11701196); 华侨大学中青年教师优秀青年科技创新人才项目(ZQN YX502); 华侨大学研究生科研创新能力培养计划项目(1511422010)
更新日期/Last Update: 2019-05-20