@Article{JCM-41-5,
author = {Yayun, Fu and Wenjun, Cai and Yushun, Wang},
title = {A Linearly-Implicit Energy-Preserving Algorithm for the Two-Dimensional Space-Fractional Nonlinear Schrödinger Equation Based on the SAV Approach},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {5},
pages = {797--816},
abstract = {<p style="text-align: justify;">The main objective of this paper is to present an efficient structure-preserving scheme,
which is based on the idea of the scalar auxiliary variable approach, for solving the two-dimensional space-fractional nonlinear Schrödinger equation. First, we reformulate the
equation as an canonical Hamiltonian system, and obtain a new equivalent system via
introducing a scalar variable. Then, we construct a semi-discrete energy-preserving scheme
by using the Fourier pseudo-spectral method to discretize the equivalent system in space
direction. After that, applying the Crank-Nicolson method on the temporal direction
gives a linearly-implicit scheme in the fully-discrete version. As expected, the proposed
scheme can preserve the energy exactly and more efficient in the sense that only decoupled
equations with constant coefficients need to be solved at each time step. Finally, numerical
experiments are provided to demonstrate the efficiency and conservation of the scheme.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2111-m2020-0177},
url = {https://global-sci.com/article/84143/a-linearly-implicit-energy-preserving-algorithm-for-the-two-dimensional-space-fractional-nonlinear-schrodinger-equation-based-on-the-sav-approach}
}