Nonlocal boundary value problems for the Schrodinger equation

被引:26
作者
Ashyralyev, Allaberen [1 ]
Sirma, Ali [2 ,3 ]
机构
[1] Fatih Univ, Dept Math, TR-34900 Istanbul, Turkey
[2] Gebez Inst Technol, Dept Math, Gebze, Kocaeli, Turkey
[3] Baccesehir Univ, Dept Math, Istanbul, Turkey
关键词
Schrodinger equation; difference schemes; stability; self adjoint operator; spectral representation;
D O I
10.1016/j.camwa.2007.04.021
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the present paper, the nonlocal boundary value problem idu/dt + Au = f (t), 0 < t < T, u(0) = Sigma(p)(m=1)alpha(m)u(lambda(m)) + phi, 0 < lambda(1) < lambda(2) < ... lambda(p) <= T for the Schrodinger equation in a Hilbert space H with the self-adjoint operator A is considered. Stability estimates for the solution of this problem are established. Two nonlocal boundary value problems are investigated. The first and second order of accuracy difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference schemes is established. In practice, stability inequalities for the solutions of difference schemes for the Schr6dinger equation are obtained. A numerical method is proposed for solving a one-dimensional Schrodinger equation with nonlocal boundary condition. A procedure involving the modified Gauss elimination method is used for solving these difference schemes. The method is illustrated by giving numerical examples. (c) 2007 Elsevier Ltd. All rights reserved.
引用
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页码:392 / 407
页数:16
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