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Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schrödinger Equations

Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schrödinger Equations
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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.

Author Details

Xiaobing Feng

Hailiang Liu

Shu Ma

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