A local energy-preserving scheme for Klein–Gordon–Schrödinger equations

doi:10.1088/1674-1056/24/5/050205

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50205-050205.doi: 10.1088/1674-1056/24/5/050205

A local energy-preserving scheme for Klein–Gordon–Schrödinger equations

蔡加祥^{a b}, 汪佳玲^a, 王雨顺^a

a Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China;
b School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

收稿日期:2014-11-28 修回日期:2014-12-09 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
Project of Graduate Education Innovation of Jiangsu Province, China (Grant No. CXLX13_366).

A local energy-preserving scheme for Klein–Gordon–Schrödinger equations

Cai Jia-Xiang (蔡加祥)^{a b}, Wang Jia-Lin (汪佳玲)^a, Wang Yu-Shun (王雨顺)^a

a Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China;
b School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

Received:2014-11-28 Revised:2014-12-09 Online:2015-05-05 Published:2015-05-05
Contact: Wang Yu-Shun E-mail:thomasjeer@sohu.com, wangyushun@njnu.edu.cn
About author:02.60.Cb; 02.70.Bf; 02.60.Lj
Supported by:
Project of Graduate Education Innovation of Jiangsu Province, China (Grant No. CXLX13_366).

摘要/Abstract

摘要： A local energy conservation law is proposed for the Klein–Gordon–Schrödinger equations, which is held in any local time–space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving (LEP) scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time–space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O(τ²+h²). The theoretical properties are verified by numerical experiments.

关键词: Klein–, Gordon–, Schrö, dinger equations, energy conservation law, local structure, convergence analysis

Abstract: A local energy conservation law is proposed for the Klein–Gordon–Schrödinger equations, which is held in any local time–space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving (LEP) scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time–space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O(τ²+h²). The theoretical properties are verified by numerical experiments.

Key words: Klein–Gordon–Schrödinger equations, energy conservation law, local structure, convergence analysis

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.70.Bf (Finite-difference methods) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)

蔡加祥, 汪佳玲, 王雨顺. A local energy-preserving scheme for Klein–Gordon–Schrödinger equations[J]. 中国物理B, 2015, 24(5): 50205-050205.

Cai Jia-Xiang (蔡加祥), Wang Jia-Lin (汪佳玲), Wang Yu-Shun (王雨顺). A local energy-preserving scheme for Klein–Gordon–Schrödinger equations[J]. Chin. Phys. B, 2015, 24(5): 50205-050205.

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A local energy-preserving scheme for Klein–Gordon–Schrödinger equations

A local energy-preserving scheme for Klein–Gordon–Schrödinger equations

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