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 - <p style="text-align: justify;">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.</p>