[1]黄蓉,翁智峰.时间分数阶Allen-Cahn方程的重心插值配点法[J].华侨大学学报(自然科学版),2022,43(4):553-560.[doi:10.11830/ISSN.1000-5013.202104060]
　HUANG Rong,WENG Zhifeng.Barycentric Interpolation Collocation Method for Time-Fractional Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2022,43(4):553-560.[doi:10.11830/ISSN.1000-5013.202104060]
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时间分数阶Allen-Cahn方程的重心插值配点法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第43卷
期数:
2022年第4期
页码:
553-560
栏目:
出版日期:
2022-07-18

文章信息/Info

Title:
Barycentric Interpolation Collocation Method for Time-Fractional Allen-Cahn Equation
文章编号:
1000-5013(2022)04-0553-08
作者:
黄蓉;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
HUANG Rong;  WENG Zhifeng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Caputo型分数阶;  Allen-Cahn方程;  Laplace变换;  重心插值配点法;  误差分析;  能量递减
Keywords:
Caputo-type fractional;  Allen-Cahn equation;  Laplace transform;  barycentric interpolation collocation method;  error analysis;  energy decline
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202104060
文献标志码:
A
摘要:
采用Laplace变换近似Caputo型分数阶导数,将分数阶方程转换成整数阶方程;然后,在时-空方向均采用重心插值配点法离散,非线性项采用Newton迭代格式求解,并给出配点格式的相容性误差分析.数值实验表明:该配点法格式具有较高精度,能满足能量递减规律.
Abstract:
The Laplace transform is uesd to approximate the Caputo-type fractional derivative and transform the time-fractional Allen-Cahn equation into the integer order case. Then, the barycentric interpolation collocation method is used to discretize integer order Allen-Cahn equation in both time and space directions, the nonlinear term is solved by Newton iteration method. Moreover, error estimates of the collocation scheme are also presented. Numerical experiments are presented to verify the high accuracy and satisfying the law of energy decline for the collocation scheme.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2021-04-29
通信作者: 翁智峰(1985-),男,博士,副教授,主要从事偏微分方程数值计算的研究.E-mail: zfwmath@163.com.
基金项目: 国家自然科学基金资助项目(11701197); 中央高校基本科研业务费专项基金资助项目(ZQN-702)
更新日期/Last Update: 2022-07-20