A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

2018 ◽  
Vol 358 ◽  
pp. 256-282 ◽  
Author(s):  
Meng Li ◽  
Xian-Ming Gu ◽  
Chengming Huang ◽  
Mingfa Fei ◽  
Guoyu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Strongly Coupled ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations ◽  
Element Method

scholarly journals A linearized conservative Galerkin–Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingfa Fei ◽  
Guoyu Zhang ◽  
Nan Wang ◽  
Chengming Huang
Keyword(s):  
Spectral Method ◽  
Numerical Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Strongly Coupled ◽  
Fully Discrete ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations ◽  
Legendre Spectral Method ◽  
Prior Bound

AbstractIn this paper, based on Galerkin–Legendre spectral method for space discretization and a linearized Crank–Nicolson difference scheme in time, a fully discrete spectral scheme is developed for solving the strongly coupled nonlinear fractional Schrödinger equations. We first prove that the proposed scheme satisfies the conservation laws of mass and energy in the discrete sense. Then a prior bound of the numerical solutions in $L^{\infty }$ L ∞ -norm is obtained, and the spectral scheme is shown to be unconditionally convergent in $L^{2}$ L 2 -norm, with second-order accuracy in time and spectral accuracy in space. Finally, some numerical results are provided to validate our theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document