Volume 26, Issue 5
Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schrödinger Equations

Xiaobing Feng ,  Hailiang Liu and Shu Ma

10.4208/cicp.2019.js60.05

Commun. Comput. Phys., 26 (2019), pp. 1365-1396.

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  • 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.

  • History

Published online: 2019-08

  • AMS Subject Headings

65M06, 65M12

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