具波动算子非线性Schrodinger方程线性化差分格式  

Linearized Difference Scheme for Nonlinear Schrodinger Equation with Wave Operator

作　　者：闫瑞娥 梁宗旗[1] YAN Ruie;LIANG Zongqi(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2020年第2期146-151,共6页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金项目(11201178,11901237);福建省自然科学基金项目(2019J01329);福建省教育厅项目(JT180262,ZC2018008)。

摘　　要：构造了具波动算子的非线性Schrodinger方程的一种线性化差分格式。即在守恒非线性差分格式的基础上,利用Taylor方法展开非线性项,引入小参数得到该方程的线性化差分格式。利用Fourier方法证明了其格式的收敛性和稳定性。最后通过数值例子验证了该方法的可信性和有效性。In this paper,the nonlinear Schrodinger equation with wave operator was constructed by a linearized difference scheme.In the conservation of nonlinear difference scheme on the basis of the method of Taylor expansion.The nonlinear term was introduced by the small parameter equation of linear difference scheme.Using the Fourier method,the convergence and stability of the format were proved.At last,through numerical example,the credibility and validity of the method were validated.

关 键 词：非线性SCHRODINGER方程 波动算子 收敛性 稳定性 线性化格式 

分 类 号：O241[理学—计算数学]