TY - JOUR
T1 - Mass- And energy-conserved numerical schemes for nonlinear Schrödinger equations
AU - Feng, Xiaobing
AU - Liu, Hailiang
AU - Ma, Shu
N1 - The work of the first author was partially supported by the NSF Grant DMS-1620168, and the work of the second author was partially supported by NSF Grant DMS-1812666. Part of the third author’s work was done during a recent visit to the University of Tennessee at Knoxville (UTK), the author would like to thank Department of Mathematics of UTK for the support and hospitality. The visit was financially supported by a scholarship from the author’s home institution, Northwestern Polytechnical University of China.
Publisher Copyright:
© 2019 Global-Science Press.
PY - 2019/11
Y1 - 2019/11
N2 - In 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.
AB - In 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.
KW - BDF schemes
KW - Finite element methods
KW - Finite time blow-ups
KW - Mass conservation and energy conservation
KW - Nonlinear Schrödinger equations
UR - https://www.scopus.com/pages/publications/85071834406
UR - https://global-sci.com/article/79862/mass-and-energy-conserved-numerical-schemes-for-nonlinear-schrodinger-equations
U2 - 10.4208/cicp.2019.js60.05
DO - 10.4208/cicp.2019.js60.05
M3 - Journal article
AN - SCOPUS:85071834406
SN - 1815-2406
VL - 26
SP - 1365
EP - 1396
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 5
ER -
