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Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations
Author(s) -
Liu Zhengguang,
Li Xiaoli,
Huang Jian
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22752
Subject(s) - cahn–hilliard equation , mathematics , stability (learning theory) , nonlinear system , fractional calculus , allen–cahn equation , energy (signal processing) , mathematical analysis , computer science , physics , partial differential equation , statistics , quantum mechanics , machine learning
Comparing with the classic phase filed models, the fractional models such as time fractional Allen–Cahn and Cahn–Hilliard equations are equipped with Caputo fractional derivative and can describe more practical phenomena for modeling phase transitions. In this paper, we construct two accurate and efficient linear algorithms for the time fractional Cahn–Hilliard and Allen–Cahn equations with general nonlinear bulk potential. The main contribution is that we have proved the unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn models and their semi‐discrete schemes carefully and rigorously. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of our proposed schemes.