一类非线性Schrodinger方程的数值解

Numerical solution to a kind of the nonlinear Schr dinger equation

对一类非线性Schr dinger方程的周期初边值问题的数值解进行了研究,对该方程提出了一种隐式差分格式,证明了该差分格式满足两个离散的守恒律,并在此基础上验证了差分格式的解在最大模范数意义下是收敛到其解析解的,且该差分格式的收敛阶为O(τ2+h 2),其中τ是时间步长,h是空间步长.

In this paper,the numerical solution to a initial periodic boundary value problem for a kind of nonlinear Schr dinger equation has been studied.We propose a new implicit difference scheme preserving conservations of the mass and energy.It is proved that the solution of difference solution converges to the exact solution of original problem with O(τ2+h 2)in L∞norm,whereτis the time-step and h is the space-step.