非线性Schrdinger方程的一个线性化紧致差分格式

A linearized compact difference scheme for nonlinear Schrdinger equation

对非线性Schrdinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性.

We propose a linearized compact difference scheme for the nonlinear Schrisdinger equation. The exist- ence of the difference solution is proved by Brouwer fixed point theorem. It is proved by the discrete energy method and the method of mathematical induction that the new scheme is uniquely solvable and convergent with fourth-order in x-direction and second-order in t-direction. Numerical results verify the precision and numerical stability of the proposed scheme.