We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L1 strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid L1-CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order 2 — γ in time, where 0 < γ < 1 is the order of the Caputo fractional derivative involved. It is proved rigorously that the hybrid numerical method accomplished is unconditionally stable in the Fourier sense. Numerical experiments are carried out with typical testing problems to validate the effectiveness of the new algorithms.

我们考虑非线性时间分数薛定ding方程（NTFSE）的高精度方案。虽然采用L1策略在时间方向上逼近Caputo分数导数，但紧凑CCD有限差分方法已纳入空间。成功实现了一种高效的L 1-CCD混合方法。这个线性化方案的精度是在空间六阶，和订单2 - γ在时间，其中，0 < γ <1是Caputo分数衍生物参与的顺序。严格证明，所完成的混合数值方法在傅立叶意义上是无条件稳定的。针对典型的测试问题进行了数值实验，以验证新算法的有效性。