Convergence of an energy-conserving scheme for nonlinear space fractional Schrodinger equations with wave operator
Cheng, Xiujun 1Qin, Hongyu 2Zhang, Jiwei2
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作者信息
1. Zhejiang Sci Tech Univ
2. Wuhan Univ
折叠
Abstract
This paper focuses on the construction and analysis of the energy-conserving numerical schemes for the generalized nonlinear space fractional Schrodinger equations with wave operator. Combining the scalar auxiliary variable (SAV) approach, we present an energy-conserving and linearly implicit scheme, while the previous conservative schemes are generally fully implicit. The energy-conserving property, boundedness and convergence of the numerical solution of the fully discrete scheme are derived for one and multi-dimensional cases. The numerical analysis is also considered. Finally, numerical examples on several fractional models illustrate that the proposed scheme can guarantee conservation of the system energy and confirm our theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
Key words
Nonlinear space fractional Schrodinger equation with wave operator/Scalar auxiliary variable approach/Energy-conserving schemes/Convergence/MODELING LIGHT BULLETS/COMPACT ADI SCHEME/SINE-GORDON/DIFFERENCE SCHEME/NUMERICAL SCHEME/APPROXIMATION
NSTL
Elsevier