第一类导数非线性Schrdinger方程的高阶差分格式  

High-order difference scheme for the first-type derivative nonlinear Schrdinger equation

作　　者：李书存[1] 石方圆 

机构地区：[1]北京信息科技大学理学院,北京100192 [2]河北师范大学数学与信息科学学院,石家庄050024

出　　处：《北京信息科技大学学报（自然科学版）》2016年第6期78-83,共6页Journal of Beijing Information Science and Technology University

摘　　要：利用Taylor展开法,给出了求解第一类导数非线性Schrdinger方程的五点四阶有限差分格式,该格式在空间上保持4阶精度,在时间上保持2阶精度。为了观察格式的适用性,将格式推广到了5阶Kd V方程。数值算例比较了该格式与Crank-Nicolson格式,验证了格式的精度阶,并给出了2个单孤子碰撞的数值模拟。A high-order finite difference scheme for the first type derivative nonlinear Schrtidinger equation is given by using the Taylor expansion. This scheme has fourth-order accuracy in space and second-order accuracy in time. In order to observe the applicability of the scheme, the scheme is extended to solve the fifth-order KdV equation. The scheme is compared with the Crank-Nicolson scheme by the numerical experiments. Numerical experiments test the accuracy order of these schemes. The numerical simulation of binary collision is discussed.

关 键 词：导数非线性Schrdinger方程 5阶KdV方程 差分格式 孤子碰撞 

分 类 号：O175.29[理学—数学]