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A Linearly-Implicit Energy-Preserving Algorithm for the Two-Dimensional Space-Fractional Nonlinear Schrödinger Equation Based on the SAV Approach

A Linearly-Implicit Energy-Preserving Algorithm for the Two-Dimensional Space-Fractional Nonlinear Schrödinger Equation Based on the SAV Approach
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Year:    2023

Author:    Yayun Fu, Wenjun Cai, Yushun Wang

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 797–816

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2111-m2020-0177

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 797–816

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Fractional nonlinear Schrödinger equation Hamiltonian system Scalar auxiliary variable approach Structure-preserving algorithm.

Author Details

Yayun Fu

Wenjun Cai

Yushun Wang

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