非线性Schrodinger方程的守恒谱方法与拟谱方法

Spectral and Pseudo-spectral Methods for a Nonlinear Schrdinger Equation

本文考察一类非线性SchrSdinger方程的谱方法与拟谱方法,构造了一类无条件稳定的全离散格式,证明了L^2模的收敛性与稳定性。该全离散格式为线性方程组,它既具备Crank-Nicolson格式(非线性方程组)的稳定性,又具备相同的精度,容易在计算机上实现。所以,较Crank-Nic01son格式优越。最后讨论了一致模的收敛性与稳定性。

In this paper, an unconditionally stable spectral and pseudo-spectral methods for a nonlinear Schrdinger equation are presented. Convergence and stability in L^2-norm are proved for both spectral and pseudo-spectral approximations. The pseudo-spectral method which is an algebrically linear system is possessed of the same accuracy and stability of Crank-Nicolson scheme which is an algebrically nonlinear system. And it is easily performed on computers. Therefore, the author's schemes are better than Crank-Nicolson scheme. Moreover, convergence and stability in uniform norm are discussed.