An efficient numerical approach to solve Schrödinger equations with space fractional derivative

We design and analyze an efficient numerical approach to solve the coupled Schrodinger equations with space-fractional derivative. The numerical scheme is based on leap-frog in time direction and Fourier method in spatial direction. The advantage of the numerical scheme is that only a linear equation needs to be solved for each time step size, and we proved that the energy and mass of space-fractional coupled Schrodinger equations (SFCSEs) are conserved in the case of full-discrete scheme. Moreover, we also analyze the error estimate of the numerical scheme, and numerical solutions converge with the order O(ot2+N-s) in L-2 norm. Numerical examples are illustrated to verify the theoretical results.