A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations

A fourth-order implicit-explicit time-discretization scheme based on the exponential time differencing approach with a fourth-order compact scheme in space is proposed for space fractional nonlinear Schrödinger equations. The stability and convergence of the compact scheme are discussed. It is shown that the compact scheme is fourth-order convergent in space and in time. Numerical experiments are performed on single and coupled systems of two and four fractional nonlinear Schrödinger equations. The results demonstrate accuracy, efficiency, and reliability of the scheme. A linearly implicit conservative method with the fourth-order compact scheme in space is also considered and used on the system of space fractional nonlinear Schrödinger equations.