A numerical method for two-dimensional Schrodinger equation using collocation and radial basis functions

被引：152

作者：

Dehghan, Mehdi ^{[1
]}

Shokri, Ali ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 54卷 / 01期

关键词：

two-dimensional Schrodinger equation; collocation; Radial Basis Function (RBF); Multiquadrics (MQ); Thin Plate Splines (TPS);

D O I：

10.1016/j.camwa.2007.01.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a numerical scheme to solve the two-dimensional (213) time-dependent Schrodinger equation using collocation points and approximating the solution using multiquadrics (MQ) and the Thin Plate Splines (TPS) Radial Basis Function (RBF). The scheme works in a similar fashion as finite-difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：136 / 146

页数：11

共 50 条

[1] A meshless symplectic method for two-dimensional Schrodinger equation with radial basis functions
Zhang, Shengliang
Chen, Siyan
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (09) : 2143 - 2150
[2] A numerical method for KdV equation using collocation and radial basis functions
Mehdi Dehghan
Ali Shokri
Nonlinear Dynamics, 2007, 50 : 111 - 120
[3] A numerical method for KdV equation using collocation and radial basis functions
Dehghan, Mehdi
Shokri, Ali
NONLINEAR DYNAMICS, 2007, 50 (1-2) : 111 - 120
[4] A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
Dehghan, Mehdi
Shokri, Ali
MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 79 (03) : 700 - 715
[5] NUMERICAL STUDIES ON TWO-DIMENSIONAL SCHRODINGER EQUATION BY CHEBYSHEV SPECTRAL COLLOCATION METHOD
Abdur, Rashid
Ismail, Ahmad Izani Bin Md
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2011, 73 (01): : 101 - 110
[6] A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional ZK–BBM Equation
Zabihi F.
Saffarian M.
International Journal of Applied and Computational Mathematics, 2017, 3 (4) : 4001 - 4013
[7] A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
Shokri, Ali
Dehghan, Mehdi
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2012, 84 (04): : 333 - 358
[8] A numerical method for one-dimensional nonlinear Sine-Gordon equation using collocation and radial basis functions
Dehghan, M.
Shokri, Ali
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (02) : 687 - 698
[9] SOLUTION OF THE TWO-DIMENSIONAL TELEGRAPH EQUATION VIA THE LOCAL RADIAL BASIS FUNCTIONS METHOD
Niknam, Sepideh
Adibi, Hojatollah
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2022, 12 (01): : 120 - 135
[10] A numerical method for heat transfer problems using collocation and radial basis functions
Zerroukat, M
Power, H
Chen, CS
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1998, 42 (07) : 1263 - 1278

← 1 2 3 4 5 →