[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):133-140.[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):133-140.[doi:10.11830/ISSN.1000-5013.201806043]
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重心插值配点法求解Allen-Cahn方程()
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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1期
页码:
133-140
栏目:
出版日期:
2019-01-20

文章信息/Info

Title:
Barycentric Interpolation Collocation Method for Allen-Cahn Equation
文章编号:
1000-5013(2019)01-0133-08
作者:
翁智峰 姚泽丰 赖淑琴
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WENG Zhifeng YAO Zefeng LAI Shuqin
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Allen-Cahn方程 重心插值配点法 Chebyshev点族 Newton迭代格式 能量递减
Keywords:
Allen-Cahn equation barycentric interpolation collocation method Chebyshev nodes Newton iterative method energy decline
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.201806043
文献标志码:
A
摘要:
利用重心插值配点法(重心Lagrange插值配点法和重心有理插值配点法)构造包含时间、空间变量的近似函数,给定Chebyshev点族;将重心插值配点法代入Allen-Cahn方程及定解条件,得到离散方程组,并采用Newton迭代格式求解方程组.数值算例表明:文中的配点法具有较高精度;利用2种配点法的能量函数满足能量递减规律.
Abstract:
Barycentric interpolation collocation method(barycentric Lagrange interpolation collocation method and Centroid rational interpolation collocation method)is proposed in this paper for the Allen-Cahn equation. By this barycentric interpolation collocation method to construct approximate time and space function based on Chebyshev nodes, we use Newton iteration method to solve Allen-Cahn equation for nonlinear terms and obtain the discrete equations.Numerical examples show that the barycentric interpolation collocation method has high precision and the energy function satisfies the energy decrement law.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2018-06-25
通信作者: 翁智峰(1985-),男,讲师,博士,主要从事偏微分方程数值解的研究.E-mail:zfwmath@163.com.
基金项目: 国家自然科学基金资助项目(11701197); 华侨大学中青年教师优秀青年科技创新人才项目(ZQN-YX502)
更新日期/Last Update: 2019-01-20