分数阶Cahn⁃Hilliard方程的高效数值算法  

An Efficient Numerical Algorithm for Fractional Cahn⁃Hilliard Equations

作　　者：汪精英 翟术英 WANG Jingying;ZHAI Shuying(School of Mathematical Sciences,Huaqiao University,Quanzhou,Fujian 362021,P.R.China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《应用数学和力学》2021年第8期832-840,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11701196);福建省自然科学基金(2020J01074)。

摘　　要：给出了时空分数阶Cahn⁃Hilliard方程的一个高效数值算法.首先,利用Laplace变换将时空分数阶Cahn⁃Hilliard方程转化为空间分数阶Cahn⁃Hilliard方程;然后,结合Fourier谱方法和有限差分法得到一个时间二阶、空间谱精度的高效数值格式;最后,通过数值实验验证本文数值算法的有效性,并验证其满足能量耗散性质和质量守恒定律.An efficient numerical algorithm for the time⁃space fractional Cahn⁃Hilliard equation was proposed.Firstly,the time⁃space fractional Cahn⁃Hilliard equation was converted into the spatial fractional Cahn⁃Hilliard equation through the Laplace transform.Then,by means of the Fourier spectral method combined with the fi⁃nite difference method,an efficient numerical scheme with 2nd⁃order convergence in time and spectral accura⁃cy in space was obtained.Finally,the validity of the proposed algorithm was verified by numerical experiments.The algorithm satisfies the energy dissipation law and the mass conservation law.

关 键 词：分数阶Cahn⁃Hilliard方程 LAPLACE变换 FOURIER谱方法 有限差分法 能量耗散 质量守恒 

分 类 号：O242[理学—计算数学]