An arbitrarily high-order energy-stabilized Adams–Bashforth-type-SAV scheme for the Allen–Cahn equation

Abstract

For the Allen–Cahn equation, it is highly desirable to develop numerical schemes that achieve both high-order temporal accuracy and energy stability. In this work, we propose a high-order energy-stable scheme by combining an explicit time integration method inspired by the Adams–Bashforth method with the scalar auxiliary variable (SAV) framework. The resulting time-stepping scheme is capable of attaining arbitrarily high orders of accuracy while preserving energy stability, a property that is rigorously proven in this paper. Numerical experiments are conducted to validate the stability and convergence behavior of the proposed method.