Open AccessSAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations
Author(s) -
Chunye Gong,
Mianfu She,
Wanqiu Yuan,
Dan Zhao
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022049
Subject(s) - discretization , mathematics , legendre polynomials , galerkin method , nonlinear system , sobolev space , mathematical analysis , convergence (economics) , scalar (mathematics) , scheme (mathematics) , geometry , physics , quantum mechanics , economics , economic growth
In this paper, a fully discrete scheme is proposed to solve the nonlinear Schrödinger-Possion equations. The scheme is developed by the scalar auxiliary variable (SAV) approach, the Crank-Nicolson temproal discretization and the Galerkin-Legendre spectral spatial discretization. The fully discrete scheme is proved to be mass- and energy- conserved. Moreover, unconditional energy stability and convergence of the scheme are obtained by the use of the Gagliardo-Nirenberg and some Sobolev inequalities. Numerical results are presented to confirm our theoretical findings.