A fast and efficient numerical algorithm for Swift–Hohenberg equation with a nonlocal nonlinearity

Abstract A high-order accurate fast explicit operator splitting scheme for the Swift–Hohenberg equation with a nonlocal nonlinearity is presented in this paper. We discretize the Swift–Hohenberg equation by a Fourier spectral method in space and an operator splitting scheme with second-order accurate in time, respectively. The second-order strong stability preserving Runge–Kutta (SSP-RK) method is presented to deal with the nonlinear part. The numerical simulations including the convergence and stability test of the proposed scheme are performed to demonstrate the efficiency of our proposed method.