| 一类非线性Schr dinger方程的高精度守恒数值格式 |
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| 作者单位： | 辽宁石油化工大学理学院，中国海洋大学数学系 抚顺 113001，青岛 266071 |
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| 摘 要： | 1引言本文讨论下面非线性Schr(?)dinger方程(NLS)方程的初边值问题:i(?)u/(?)t (?)~2u/(?)x~2 2|u~2|u=0,(1) u(x_l,t)=u(x_r,t)=0,t>0,(2) u(x,0)=u_0(x),x_l≤x≤x_r,(3)其中u(x,t)是复值函数,u_0(x)为已知的复值函数,i~2=-1.该问题有着如下的电荷与能量守恒关系:
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A HIGH ACCURATE AND CONSERVATIVE NUMERICAL SCHEME FOR NONLINEAR SCHR DINGER EQUATION |
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| Authors: | Zhang Rongpei |
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| Abstract: | In this paper,we present a new high accurate and conservative numer- ical scheme for nonlinear SchrSdinger type equations.The scheme conserves the en- ergy and charge of systems,and its convergence and stability are proved.By means of numerical computing,we get the conclusion that the new difference scheme is much better than the other schemes. |
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| Keywords: | NLS equation difference scheme high precision conservation convergence stability |
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