Diffusion in Allen-Cahn equation: Normal vs anomalous

It is known that the anomalous diffusion can be well characterized by the fractional derivatives. In this paper, the Allen-Cahn equations with different kinds of time fractional derivatives are numerically studied. The numerical solutions of the Allen-Cahn equations are obtained by using Euler method or L1 method to approximate the time derivative and the finite element method in the space direction. Finally, the influences of time derivatives on the solutions of the considered models are observed and discussed.

Automated summary

This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.