非线性Schr■dinger方程的一种数值模拟方法  

A Numerical Simulation Method of Nonlinear Schr■dinger Equation

作　　者：张静[1] 张鲁明[2] 陈娟[3] 

机构地区：[1]天津职业大学,天津300402 [2]南京航空航天大学,南京210016 [3]常熟理工学院,常熟215500

出　　处：《数学物理学报（A辑）》2007年第6期1111-1117,共7页Acta Mathematica Scientia

摘　　要：该文通过对非线性Schr■dinger方程增加耗散项,提出了一种新的三层线性差分格式.证明了该格式满足连续方程所具有的两个守恒量及收敛性和稳定性.通过数值例子与已知格式进行比较,结果表明该格式计算简单且具有较高精度.In this paper, the authors propose a three-level and linear difference scheme through adding a dissipation term to the nonlinear SchrSdinger equation. It is proved that the scheme preserves two conservative quantities that the continuous equation owns. Comparing it with the known schemes by the numerical examples, the authors get the conclusion that the scheme is computed easily and has higher precision.

关 键 词：NLS方程 耗散项 差分格式 收敛性 稳定性. 

分 类 号：O241.82[理学—计算数学]