论文部分内容阅读
用拟Shannon区间小波解非线性薛定谔方程,为数值解提供了又一有力工具.简要分析了分步方法的一般形式,得出了分步小波方法的算法公式.说明了色散算子矩阵是Toeplitz矩阵,分步小波方法的运算量主要来自色散段中Toeplitz矩阵向量积.该方法减小了该To-eplitz矩阵的存储空间,从而提高了运算速度.以解析解为准,给出了基于拟Shannon区间小波的分步小波方法的相对误差.结果表明,与以往基于Daubeches小波的分步小波方法相比,精确性有了较大提高.“,”Quasi-Shannon interval wavelet was used to solve the nonlinear Schr ?dinger equation , which provided another powerful tool for numerical solution of the equation .The general form of split -step algorithm was studied briefly.The dispersion matrix is Toeplitz matrix , and most of the calculation came from Toeplitz Matrix -Vector Product.This method abated the memory space for Toeplitz Matrix to improve calculating speed .Finally, with the analytic solution being the standard , the accuracy of split -step Wavelet method based on Quasi -Shannon interval wavelet was given .The results show that compared with split -step wavelet method based on Daubechies wavelet, the accuracy has improved greatly .