2019/11/18 by Yayun Fu, Fu, Yayun, Wenjun Cai +3
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1911.07379
24 pages,7 figures
arxiv created 2019/11/18 · openalex publication_date 2019/11/18 · arxiv updated 2019/11/19 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28
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 space fractional nonlinear Schrödinger equation. First, we reformulate the equation as a 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 linear 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 effectiveness and conservation of the scheme.