Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn-Hilliard and Allen-Cahn equations

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.

Automated summary

Two accurate and efficient linear algorithms are proposed for the time fractional Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potential, demonstrating unconditional energy stability and numerical simulations verify their accuracy and efficiency in 2D and 3D.