利用Laplace变换求解分数阶Allen-Cahn方程  

Numerical Solution of Fractional Allen-Cahn Equation by Laplace Transform

作　　者：汪精英 邓杨芳 翟术英 WANG Jingying;DENG Yangfang;ZHAI Shuying(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2020年第4期549-554,共6页Journal of Huaqiao University(Natural Science)

基　　金：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(ZQNYX502);华侨大学研究生科研创新能力培养计划项目(18013070013)。

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.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.

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 

分 类 号：O241.8[理学—计算数学]