A Flexible Symplectic Scheme for Two-Dimensional Schrodinger Equation with Highly Accurate RBFs Quasi-Interpolation

被引：1

作者：

Zhang, Shengliang ^{[1
]}

Zhang, Liping ^{[2
]}

机构：

[1] Nanjing Forestry Univ, Coll Econ & Management, Nanjing, Jiangsu, Peoples R China

[2] Zhejiang Univ Technol, Dept Math, Hangzhou 310023, Zhejiang, Peoples R China

来源：

FILOMAT | 2019年 / 33卷 / 17期

关键词：

Two-dimensional Schrodinger equation; Cubic multiquadric quasi-interpolation; Symplectic integrator; Hamiltonian PDEs; Meshless method; ALGORITHM; COLLOCATION; INTEGRATION;

D O I：

10.2298/FIL1917451Z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on highly accurate multiquadric quasi-interpolation, this study suggests a meshless symplectic procedure for two-dimensional time-dependent Schrodinger equation. The method is high-order accurate, flexible with respect to the geometry, computationally efficient and easy to implement. We also present a theoretical framework to show the conservativeness and convergence of the proposed method. As the numerical experiments show, it not only offers a high order accuracy but also has a good performance in the long time integration.

引用

页码：5451 / 5461

页数：11

共 29 条

[1]

[Anonymous], 1994, APPL MATH MATH COMPU

[2]

[Anonymous], 2005, Wave Propag. Underw. Acoust., DOI [DOI 10.1007/3-540-08527-0_5, 10.1007/3-540-08527-05, DOI 10.1007/3-540-08527-05, DOI 10.1007/3-540-08527-0]

[3] Numerically absorbing boundary conditions for quantum evolution equations [J].

Arnold, A .

VLSI DESIGN, 1998, 6 (1-4) :313-319

[4] Multiquadric B-splines [J].

Beatson, RK ;

Dyn, N .

JOURNAL OF APPROXIMATION THEORY, 1996, 87 (01) :1-24

[5] UNIVARIATE MULTIQUADRIC APPROXIMATION - QUASI-INTERPOLATION TO SCATTERED DATA [J].

BEATSON, RK ;

POWELL, MJD .

CONSTRUCTIVE APPROXIMATION, 1992, 8 (03) :275-288

[6] Numerical methods for Hamiltonian PDEs [J].

Bridges, Thomas J. ;

Reich, Sebastian .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (19) :5287-5320

[7]

Cano B, 2006, NUMER MATH, V103, P197, DOI [10.1007/s00211-006-0680-3, 10.1007/S00211-006-0680-3]

[8] Exponential convergence and H-c multiquadric collocation method for partial differential equations [J].

Cheng, AHD ;

Golberg, MA ;

Kansa, EJ ;

Zammito, G .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2003, 19 (05) :571-594

[9] A numerical method for two-dimensional Schrodinger equation using collocation and radial basis functions [J].

Dehghan, Mehdi ;

Shokri, Ali .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (01) :136-146

[10] Symplectic finite difference approximations of the nonlinear Klein-Gordon equation [J].

Duncan, DB .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1742-1760

← 1 2 3 →