期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 243, 期 -, 页码 382-399出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.03.007
关键词
Nonlinear Schrodinger equation; Compact and conservative difference scheme; A priori estimate; Unconditional convergence
资金
- National Natural Science Foundation of China [11126292, 11201239]
In this paper, a fourth-order compact and energy conservative difference scheme is proposed for solving the two-dimensional nonlinear Schrodinger equation with periodic boundary condition and initial condition, and the optimal convergent rate, without any restriction on the grid ratio, at the order of O(h(4) + tau(2)) in the discrete L-2-norm with time step tau and mesh size h is obtained. Besides the standard techniques of the energy method, a new technique and some important lemmas are proposed to prove the high order convergence. In order to avoid the outer iteration in implementation, a linearized compact and energy conservative difference scheme is derived. Numerical examples are given to support the theoretical analysis. (C) 2013 Elsevier Inc. All rights reserved.
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