[1]汪精英,邓杨芳,翟术英.利用Laplace变换求解分数阶Allen-Cahn方程[J].华侨大学学报(自然科学版),2020,41(4):549-554.[doi:10.11830/ISSN.1000-5013.201910013]
 WANG Jingying,DENG Yangfang,ZHAI Shuying.Numerical Solution of Fractional Allen-Cahn Equation byLaplace Transform[J].Journal of Huaqiao University(Natural Science),2020,41(4):549-554.[doi:10.11830/ISSN.1000-5013.201910013]
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利用Laplace变换求解分数阶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41卷
期数:
2020年第4期
页码:
549-554
栏目:
出版日期:
2020-07-20

文章信息/Info

Title:
Numerical Solution of Fractional Allen-Cahn Equation byLaplace Transform
文章编号:
1000-5013(2020)04-0549-06
作者:
汪精英 邓杨芳 翟术英
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WANG Jingying DENG Yangfang ZHAI Shuying
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
分数阶Allen-Cahn方程 Caputo型分数阶导数 Laplace变换 算子分裂 能量递减
Keywords:
fractional Allen-Cahn equation Caputo-type fractional derivative Laplace transform operator splitting method energy decline
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.201910013
文献标志码:
A
摘要:
考虑Caputo型分数阶Allen-Cahn方程的高效数值算法,利用Laplace变换将其转化为整数阶Allen-Cahn方程.利用算子分裂方法进一步将其分解为热传导方程和非线性方程.其中,非线性方程精确求解,热传导方程采用二阶差分方法求解.数值实验表明了所给格式的有效性.
Abstract:
An efficient numerical algorithm for Caputo-type fractional Allen-Cahne quation is considered. Firstly, the Laplace transform is used to transform it into integer order Allen-Cahn equation, and then the operator splitting method is used to decompose into heat conduction equation and nonlinear equation. The nonlinear equation is solved analytically and the heat conduction equation is solved using second-order finite difference method. Numerical experiments are presented to confirm the efficiency of the proposed method.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2019-10-15
通信作者: 翟术英(1986-),女,副教授,博士,主要从事偏微分方程数值解及理论的研究.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(ZQNYX5 02); 华侨大学研究生科研创新能力培养计划项目(18013070013)
更新日期/Last Update: 2020-07-20