Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation

Abstract

In this paper, we propose a second-order fast explicit operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in $$L^2$$ -norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.