Abstract
A numerical simulation technique for the coupled system of variable -order time fractional nonlinear Schro center dot dinger equations is developed in this paper using the finite difference/spectral method. The finite difference method is adapted to dis-cretize the variable-order Caputo time-fractional derivative, and the spectral technique is used for spatial approximation. The significant advantage of the proposed algorithm is that the iterative procedure is not used to implement the nonlinear term in the cou-pled system. In addition, numerical experiments are performed in order to verify the accuracy of the method.