TY - JOUR
T1 - Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schrödinger Equations
AU - Feng , Xiaobing
AU - Liu , Hailiang
AU - Ma , Shu
JO - Communications in Computational Physics
VL - 5
SP - 1365
EP - 1396
PY - 2019
DA - 2019/08
SN - 26
DO - http://doi.org/10.4208/cicp.2019.js60.05
UR - https://global-sci.org/intro/article_detail/cicp/13268.html
KW - Nonlinear Schrödinger equations, mass conservation and energy conservation, BDF
schemes, finite element methods, finite time blow-ups.
AB - <p style="text-align: justify;">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.</p>