An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain

被引：23

作者：

Han, Houde ^{[1
]}

Zhang, Zhiwen ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 07期

关键词：

Artificial Boundary Condition (ABC); Unbounded domain; Energy method; Fast algorithm; Discrete Artificial Boundary Condition (DABC); ABSORBING BOUNDARY-CONDITIONS; SCHRODINGER-EQUATION; APPROXIMATIONS; SIMULATION; SCHEMES; SYSTEMS; WAVES;

D O I：

10.1016/j.apnum.2008.10.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution of the one-dimensional Klein-Gordon equation on an unbounded domain is analyzed in this paper. Two artificial boundary conditions are obtained to reduce the original problem to an initial boundary value problem on a bounded computational domain, which is discretized by an explicit difference scheme. The stability and convergence of the scheme are analyzed by the energy method. A fast algorithm is obtained to reduce the Computational cost and a discrete artificial boundary condition (DABC) is derived by the Z-transform approach. Finally, we illustrate the efficiency of the proposed method by several numerical examples. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1568 / 1583

页数：16

共 25 条

[1]

Andrews L.C., 1998, Special Functions of Mathematics for Engineers

[2]

[Anonymous], 2004, TABLE INTEGRALS SERI

[3] Numerical schemes for the simulation of the two-dimensional Schrodinger equation using non-reflecting boundary conditions [J].

Antoine, X ;

Besse, C ;

Mouysset, V .

MATHEMATICS OF COMPUTATION, 2004, 73 (248) :1779-1799

[4] Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrodinger equation [J].

Antoine, X ;

Besse, C .

JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 188 (01) :157-175

[5] Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics [J].

Arnold, A ;

Ehrhardt, M .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 145 (02) :611-638

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

Arnold, A .

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

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

Duncan, DB .

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

[8] A dynamic atomistic-continuum method for the simulation of crystalline materials [J].

E, WN ;

Huang, ZY .

JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 182 (01) :234-261

[9] Fast calculation of energy and mass preserving solutions of Schrodinger-Poisson systems on unbounded domains [J].

Ehrhardt, M ;

Zisowsky, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 187 (01) :1-28

[10]

Ehrhardt M., 1997, Z ANGEW MATH MECH, V77, P543

← 1 2 3 →