A fast and efficient numerical algorithm for fractional Allen–Cahn with precise nonlocal mass conservation

Abstract

In this paper, based on operator splitting method and a fourth order compact scheme for Riesz derivative, we propose a fast and efficient numerical algorithm with order O(τ2+h4) to solve the space fractional conservative Allen–Cahn equation with a space–time dependent nonlocal Lagrange multiplier, where τ is the time step and h is the space grid size. The method is very easy to implement and non-iterative, where one only needs to solve three decoupled equations at each time step. The mass conservation and discrete maximum principle of the numerical algorithm are analyzed theoretically. Numerical experiments are presented to confirm the accuracy and efficiency of the proposed method.