TY - JOUR T1 - Conservative Numerical Schemes for the Nonlinear Fractional Schrödinger Equation AU - Wu , Longbin AU - Ma , Qiang AU - Ding , Xiaohua JO - East Asian Journal on Applied Mathematics VL - 3 SP - 560 EP - 579 PY - 2021 DA - 2021/05 SN - 11 DO - http://doi.org/10.4208/eajam.110920.060121 UR - https://global-sci.org/intro/article_detail/eajam/19141.html KW - Crank-Nicolson Fourier collocation method, nonlinear fractional Schrödinger equation, conservation laws, existence and uniqueness, convergence. AB -

This paper deals with the Crank-Nicolson Fourier collocation method for the nonlinear fractional Schrödinger equation containing a fractional derivative. We prove that at each discrete time the method preserves the discrete mass and energy conservation laws. The existence, uniqueness and convergence of the numerical solution are also investigated. In particular, we show that the method has the second-order accuracy in time and the spectral accuracy in space. Since the proposed schemes are implicit, they are solved by an iteration algorithm with FFT. Two examples illustrate the efficiency and accuracy of the numerical schemes.