In the paper, the high-order conservative schemes are presented for space fractional nonlinear Schrödinger equation. First, we give two class high-order difference schemes for fractional Risze derivative by compact difference method and extrapolating method, and show the convergence analysis of the two methods. Then, we apply high-order conservative difference schemes in space direction, and Crank-Nicolson, linearly implicit and relaxation schemes in time direction to solve fractional nonlinear Schrödinger equation. Moreover, we show that the arising schemes are uniquely solvable and approximate solutions converge to the exact solution at the rate $O({\tau }^2+h^4)$, and preserve the mass and energy conservation laws. Finally, we given numerical experiments to show the efficiency of the conservative finite difference schemes.

在本文中，提出了空间分数阶非线性薛定ding方程的高阶保守方案。首先，通过紧致差分法和外推法给出了分数Risze导数的两类高阶差分格式，并给出了两种方法的收敛性分析。然后，我们在空间方向上应用高阶保守差分方案，并在时间方向上应用Crank-Nicolson，线性隐式和松弛方案来求解分数阶非线性Schrödinger方程。此外，我们证明了出现的方案是唯一可解的，并且近似解以一定的速率收敛到精确解。$Ø（{\tau }^{\mathrm{2个}}+H^4）$，并遵守《大众和节能法》。最后，我们通过数值实验证明了保守有限差分方案的有效性。