SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations

Chunye Gong; Mianfu She; Wanqiu Yuan; Dan Zhao; Chunye Gong; Mianfu She; Wanqiu Yuan; Dan Zhao

doi:10.3934/era.2022049

Electronic Research Archive

2022, Volume 30, Issue 3: 943-960. doi: 10.3934/era.2022049

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SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations

1.
School of Computer Science, National University of Defense Technology, Changsha 410073, China
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received: 29 December 2021 Revised: 20 February 2022 Accepted: 22 February 2022 Published: 04 March 2022

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.
- nonlinear Schrödinger-Possion equations,
- energy stability,
- error estimates,
- Galerkin-Legendre spectral method,
- scalar auxiliary variable (SAV)
Citation: Chunye Gong, Mianfu She, Wanqiu Yuan, Dan Zhao. SAV Galerkin-Legendre spectral method for the nonlinear Schrödinger-Possion equations[J]. Electronic Research Archive, 2022, 30(3): 943-960. doi: 10.3934/era.2022049

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Abstract

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.

References

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