中文摘要：

在空间方向用高阶紧致格式离散,时间方向分别用CNI格式、Richardson格式和分裂步CNI格式离散,得到了长短波方程的一些数值格式.这些格式在时间方向是二阶收敛的,空间方向是四阶的,而用到的模版与二阶中心差分格式是一样的.数值结果表明,与中心格式相比,新提出的格式较已有格式计算效率更高.同时,从数值结果可以猜测CNI格式和分裂步CNI格式能够保持原问题的一些守恒量.

英文摘要：

By applying high order compact approximation to the space direction and combining with some numerical methods to the time direction,some high order compact schemes are proposed for the long-short wave equations,which include the Crank-Nicolson implicit（CNI） scheme,the Richardson scheme,and the split-step CNI scheme.It is observed that they are of second order in time and fourth order in space with the same stencil as the second order central approximation.Numerical illustrations verify the results.Compared to the central scheme,the new schemes are of higher accuracy and more efficient in computational cost.It is conjectured from the numerical results that the CNI scheme and the split-step CNI scheme can preserve some conservation laws.