Stable second-order schemes for the space-fractional Cahn-Hilliard and Allen-Cahn equations

被引：23
|
作者：
Bu, Linlin [1 ]
Mei, Liquan [1 ]
Hou, Yan [2 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] Shenzhen Yun Zhong Fei Network Technol Co Ltd, Shenzhen 518000, Guangdong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 11期
关键词：
Fractional Cahn-Hilliard equation; Fractional Allen-Cahn equation; Convex splitting; Mass conservative; The unique solvability; Energy stable; FINITE-DIFFERENCE SCHEME; SPLITTING METHODS; FREE-ENERGY;
D O I：
10.1016/j.camwa.2019.05.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose stable second-order numerical schemes for the fractional Cahn-Hilliard and Allen-Cahn equations, which are based on the convex splitting in time and the Fourier spectral method in space. It is shown that the scheme for the fractional Cahn-Hilliard equation preserves mass. Meanwhile, the unique solvability and energy stability of the numerical schemes for the fractional Cahn-Hilliard and Allen-Cahn equations are proved. Finally, we present some numerical experiments to confirm the accuracy and the effectiveness of the proposed methods. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3485 / 3500
页数：16
相关论文
共 50 条
  • [1] Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations
    Guan, Zhen
    Lowengrub, John
    Wang, Cheng
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) : 6836 - 6863
  • [2] Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations
    Guan, Zhen
    Lowengrub, John S.
    Wang, Cheng
    Wise, Steven M.
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 277 : 48 - 71
  • [3] Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models
    Guillen-Gonzalez, Francisco
    Tierra, Giordano
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 68 (08) : 821 - 846
  • [4] ON THE CAHN-HILLIARD/ALLEN-CAHN EQUATIONS WITH SINGULAR POTENTIALS
    Miranville, Alain
    Saoud, Wafa
    Talhouk, Raafat
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3633 - 3651
  • [5] NUMERICAL APPROXIMATIONS OF ALLEN-CAHN AND CAHN-HILLIARD EQUATIONS
    Shen, Jie
    Yang, Xiaofeng
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (04) : 1669 - 1691
  • [6] Grain sizes in the discrete Allen-Cahn and Cahn-Hilliard equations
    Grant, CP
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2001, 7 (01) : 127 - 146
  • [7] A further study on the coupled Allen-Cahn/Cahn-Hilliard equations
    Yang, Jiaqi
    Liu, Changchun
    [J]. BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)
  • [8] Stability Analysis of Several Time Discrete Schemes for Allen-Cahn and Cahn-Hilliard Equations
    He, Qiaoling
    Yan, Junping
    Abuduwaili, Abudurexiti
    [J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2023, 63 (10) : 1773 - 1786
  • [9] Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations
    Lee, Dongsun
    Kim, Junseok
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 119 : 35 - 56
  • [10] Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen-Cahn equations
    Wang, Kai
    Feng, Jundong
    Chen, Hongbo
    Xu, Changling
    [J]. ADVANCES IN CONTINUOUS AND DISCRETE MODELS, 2022, 2022 (01):
12345