@Article{EAJAM-11-3,
author = {Wu, Longbin and Qiang, Ma and Xiaohua, Ding},
title = {Conservative Numerical Schemes for the Nonlinear Fractional Schrödinger Equation},
journal = {East Asian Journal on Applied Mathematics},
year = {2021},
volume = {11},
number = {3},
pages = {560--579},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.110920.060121},
url = {https://global-sci.com/article/82526/conservative-numerical-schemes-for-the-nonlinear-fractional-schrodinger-equation}
}