An effective numerical method for the vector-valued nonlocal Allen–Cahn equation

Abstract

Nonlocal Allen–Cahn model and their numerical schemes have received great attention in the literature as nonlocal model becomes popular in various fields. Our main idea in this work is to consider the vector-valued nonlocal Allen–Cahn model, which is a coupled system of nonlinear partial differential equations. Then, with the help of the operator splitting method and finite difference method, a fully-decoupled and energy stable numerical scheme for the vector-valued nonlocal Allen–Cahn model is proposed. Furthermore, we prove the modified energy dissipation law is unconditionally guaranteed and it is closely related to classical energy up to O(τ). Finally, numerical examples are carried out to verify the efficiency and accuracy of the proposed scheme.