摘要
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Toeplitz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 Schrtidinger 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 the analytic solution being the standard, the accuracy of split - step Wavelet method based interval wavelet was given. The results show that compared with split - step wavelet method wavelet, the accuracy has improved greatly. speed. Finally, with on Quasi - Shannon based on Daubechies
作者
钟鸣宇
朱宗玖
ZHONG Ming - yu ZHU Zong - jiu(School of Mechanical Engineering and Automatization, Anhui University of Science and Technology, Huainan Anhui 232001, China)
出处
《安徽理工大学学报（自然科学版）》
CAS
2016年第5期59-62,77,共5页
Journal of Anhui University of Science and Technology:Natural Science
