Solving unsteady Schrödinger equation using the improved element-free Galerkin method
Rong-Jun Cheng(程荣军)^{1} and Yu-Min Cheng(程玉民)^{2}
1. Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Abstract By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrödinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.

Keywords:
meshless method
improved moving least-square (IMLS) approximation
improved element-free Galerkin (IEFG) method
Schrö
dinger equation
Received: 09 July 2015
Revised: 01 November 2015
Published: 05 February 2016
PACS:
02.60.Lj
(Ordinary and partial differential equations; boundary value problems)
03.65.Ge
(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171208), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY15A020007), the Natural Science Foundation of Ningbo City (Grant No. 2014A610028), and the K. C. Wong Magna Fund in Ningbo University, China.

Corresponding Authors:
Yu-Min Cheng
E-mail: ymcheng@shu.edu.cn

Cite this article:
Rong-Jun Cheng(程荣军) and Yu-Min Cheng(程玉民) Solving unsteady Schrödinger equation using the improved element-free Galerkin method 2016 Chin. Phys. B 25 020203

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