Year: 2019
Author: Xiaobing Feng, Hailiang Liu, Shu Ma
Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1365–1396
Abstract
n this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schrödinger equations. The proposed schemes all satisfy both mass and energy conservation (in a modified form for the latter). Truncation and dispersion error analyses are provided for four proposed schemes. Efficient fixed-point iterative solvers are also constructed to solve the resulting nonlinear discrete problems. As a byproduct, an efficient one-step implementation of the BDF schemes is obtained as well. Extensive numerical experiments are presented to demonstrate the convergence and the capability of capturing the blow-up time of the proposed schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2019.js60.05
Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1365–1396
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Nonlinear Schrödinger equations mass conservation and energy conservation BDF schemes finite element methods finite time blow-ups.