The high-order maximum-principle-preserving integrating factor Runge-Kutta methods for nonlocal Allen-Cahn equation

Abstract

We extend the explicit integrating factor Runge-Kutta methods coupled with non-decreasing abscissas (eIFRK+) to the nonlocal Allen-Cahn (NAC) equation. We further propose the new three-stage third-order and four-stage fourth-order eIFRK+ schemes based on the classic RK method, which can be used for a class of local and nonlocal models. In this paper, the method is mainly applied to study the NAC equation. Under a large time-step constraint, the high-order eIFRK+ schemes are demonstrated to preserve maximum bound principle, which is a crucial physical property for the NAC models. Then, the optimal error estimates in L∞(0,T;Ω)-norm are established and the asymptotic compatibility of the proposed schemes are validated. Numerical experiments are carried out to verify our theoretical results and illustrate the effectiveness of the fully discrete schemes. Moreover, by the aid of numerical simulation, we attempt to declare that the eIFRK+ schemes are energy stable under the weak time-step restriction.