The Laguerre pseudospectral method for the two-dimensional Schrodinger equation with symmetric nonseparable potentials

被引：3

作者：

Alici, Haydar ^{[1
]}

机构：

[1] Harran Univ, Dept Math, TR-63290 Sanliurfa, Turkey

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2020年 / 49卷 / 02期

关键词：

the Laguerre pseudospectral method; two dimensional Schrodinger equation; symmetric potentials; SPECTRAL METHODS; INTERPOLATION; EIGENVALUES;

D O I：

10.15672/hujms.459593

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Hermite pseudospectral method is one of the natural techniques for the numerical treatment of the problems defined over unbounded domains such as two-dimensional time-independent Schrodinger equation on the whole real plane. However, it is shown here that for the symmetric potentials, transformation of the problem over the first quadrant and the application of the Laguerre pseudospectral method reduce the cost by a factor of four when compared to the Hermite pseudospectral method.

引用

页码：539 / 552

页数：14

共 50 条

[31] A generalization of Numerov's method for the numerical solution of the Schrodinger equation in two dimensions [J].

Konguetsof, A ;

Avdelas, G ;

Simos, TE .

INTERNATIONAL CONFERENCE ON PARALLEL AND DISTRIBUTED PROCESSING TECHNIQUES AND APPLICATIONS, VOLS I-V, PROCEEDINGS, 1999, :259-264

[32] A generalization of Numerov's method for the numerical solution of the Schrodinger equation in two dimensions [J].

Avdelas, G ;

Konguetsof, A ;

Simos, TE .

COMPUTERS & CHEMISTRY, 2000, 24 (05) :577-584

[33] Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrodinger equations [J].

Zhu, Huajun ;

Chen, Yaming ;

Song, Songhe ;

Hu, Huayu .

APPLIED NUMERICAL MATHEMATICS, 2011, 61 (03) :308-321

[34] A numerical method for two-dimensional Hammerstein integral equations [J].

Micula, Sanda .

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2021, 66 (02) :267-277

[35] A note on "Quasi-analytical solution of two-dimensional Helmholtz equation" [J].

Smith, Stefan G. Llewellyn .

APPLIED MATHEMATICAL MODELLING, 2018, 54 :281-283

[36] A local hybrid kernel meshless method for numerical solutions of two-dimensional fractional cable equation in neuronal dynamics [J].

Oruc, Omer .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (06) :1699-1717

[37] Optical solitons of the (1+1)-dimensional higher-order nonlinear Schrodinger equations with PT-symmetric potentials [J].

Xu, Bijun ;

Yan, Mengyao ;

Sun, Zhichao ;

Tong, Xin .

OPTIK, 2019, 181 :1019-1022

[38] Improvements to the computation of eigenvalues and eigenfunctions of two-dimensional Schrodinger equations by constant perturbation based algorithms [J].

Baeyens, Toon ;

Van Daele, Marnix .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 412

[39] Existence and quantum calculus of weak solutions for a class of two-dimensional Schrodinger equations in C+ [J].

Xing, Yifan ;

Zhao, Jinhui .

BOUNDARY VALUE PROBLEMS, 2018, :1-10

[40] A direct numerical method for approximate solution of inverse reaction diffusion equation via two-dimensional Legendre hybrid functions [J].

Gholampoor, I. ;

Kajani, M. Tavassoli .

NUMERICAL ALGORITHMS, 2020, 83 (02) :511-528

← 1 2 3 4 5 →