A local energy-preserving scheme for Klein Gordon Schrdinger equations  

作　　者：蔡加祥 汪佳玲 王雨顺 

机构地区：[1]Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University [2]School of Mathematical Science, Huaiyin Normal University

出　　处：《Chinese Physics B》2015年第5期171-176,共6页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11201169,11271195,and 41231173);the Project of Graduate Education Innovation of Jiangsu Province,China(Grant No.CXLX13 366)

摘　　要：A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger 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.A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger 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-Schrodinger equations energy conservation law local structure convergence analysis 

分 类 号：O175[理学—数学]