Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 671–688
Abstract
This paper is concerned with numerical method for a two-dimensional time-dependent cubic nonlinear Schrödinger equation.
The approximations are obtained by the Galerkin finite element method in space in conjunction with
the backward Euler method and the Crank-Nicolson method in time, respectively. We prove optimal $L^2$ error estimates for two fully discrete schemes by using elliptic projection operator.
Finally, a numerical example is provided to verify our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.y16008
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 671–688
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18