广义非线性Schrdinger方程组的一个新的守恒差分格式

A new conservative finite difference scheme for a class of generalized nonlinear Schrdinger equations

对两类广义非线性Schrdinger方程组的初边值问题给出一种新的高精度守恒差分格式,证明了它保持原来微分方程所具有的两个守恒关系,并对差分解作出了先验估计,在此基础上证明了差分解的存在唯一性以及差分格式的稳定性和收敛性.对差分方程组,给出了追赶迭代法求解公式,并证明了差分解的收敛性.

A high order, new conservative finite difference scheme is proposed for a class of generalized nonlinear Schrodinger equations. It is proved that the scheme preserves two conservative quantities of the original equation. The prior estimation for the difference solution is made. Thereby, it is proved that the scheme is convergent and stable, and existence and uniqueness of the solution for the scheme are obtained. The Persuit - iteration method is applied to solve the finite difference equations, and the convergence of the difference solution is obtained.