Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation

Yayun Fu, Yongzhong Song and Yushun Wang

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 166, issue C, 206-223

Abstract: This paper aims to construct a numerical scheme for the damped nonlinear space fractional Schrödinger equation. First, the conservation laws of mass and energy for the continuous equation are derived. Then, based on the fractional centered difference formula, a semi-discrete scheme, which preserves the semi-discrete mass and energy conservation laws is proposed. Further applying the Crank–Nicolson method on the temporal direction gives a fully-discrete conservative scheme. Furthermore, the solvability, boundedness and convergence in the maximum norm of the numerical solutions are given. Some numerical examples are displayed to confirm the theoretical results.

Keywords: Damped nonlinear fractional Schrödinger equation; Conservative difference scheme; Stability and convergence analysis (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:166:y:2019:i:c:p:206-223

DOI: 10.1016/j.matcom.2019.05.001

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