Fast High Order and Energy Dissipative Schemes with Variable Time Steps for Time-Fractional Molecular Beam Epitaxial Growth Model

Abstract

In this paper, we propose and analyze high order energy dissipative time-stepping schemes for time-fractional molecular beam epitaxial (MBE) growth model on the nonuniform mesh. More precisely, (2−α)-order, secondorder and (3−α)-order time-stepping schemes are developed for the timefractional MBE model based on the well known L1, L2-1 σ , and L2 formulations in discretization of the time-fractional derivative, which are all proved to be unconditional energy dissipation in the sense of a modified discrete nonlocalenergy on the nonuniform mesh. In order to reduce the computational storage, we apply the sum of exponential technique to approximate the history part of the time-fractional derivative. Moreover, the scalar auxiliary variable (SAV) approach is introduced to deal with the nonlinear potential function and the history part of the fractional derivative. Furthermore, only first order method is used to discretize the introduced SAV equation, which will not affect high