Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 182, Issue 2, Pages 1780-1794Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2006.06.015
Keywords
Schrodinger equation; difference scheme; conservation; convergence
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Some new conservative finite difference schemes are presented for an initial-boundary value problem of Schrodinger equation with wave operator. They have the advantages that there are some discrete energies which are conserved respectively. The existence of the solution of the finite difference schemes are proved by Leray-Schauder fixed point theorem. And the uniqueness, stability and convergence of difference solutions with order O(h(2) + tau(2)) are proved in the energy norm. Results of numerical experiment demonstrate the efficiency of the new scheme. (c) 2006 Elsevier Inc. All rights reserved.
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