两点边值问题的拟Shannon小波数值解法  

Quasi Shannon Wavelet Numerical Solution of Two point Boundary Value Problems

作　　者：梅树立[1] 陈奎孚[1] 张森文[2] 杜承进[3] 雷廷武[4] 

机构地区：[1]中国农业大学工程基础科学部 [2]暨南大学应用力学研究所 [3]中国农业大学计算机网络中心 [4]中国科学院,水利部水土保持研究所

出　　处：《中国农业大学学报》2002年第2期12-16,共5页Journal of China Agricultural University

基　　金：国家自然科学基金资助项目 ;中科院;水利部水土保持研究所国家重点实验室资助课题

摘　　要：用拟 Shannon尺度函数作为权函数构造了两点边值问题的小波配置法 ,空间导数采用拟小波数值格式离散。在此基础上 ,进一步给出了小波配置解的外推方法。外推法是一种简单易行而精度又很高的数值方法 ,而且网格步长 h的选取可以和小波配置法中配置点的选取采用相同的策略 ,所以可以很方便地将两点边值问题的小波配置解进行外推 ,以提高解的精度。数值算例表明 ,拟小波配置法适合于求解具有大梯度解的问题 。A quasi Shannon wavelet collocation method for two point boundary value problems was constructed. The quasi wavelet based numerical method was used to discrete the spatial deriatives. The extrapolation method for quasi Shannon wavelet collocation solution was provided. The same strategy can be taken between Shannon wavelet collocation method and extrapolation method in choosing mesh spacing, it is easy to improve computational accuracy by combining these two methods. The numerical solution of examples showed that quasi Shannon wavelet collocation method is successful in computing of the problems possessed heavy gradient solutions, and the extrapolation method is helpful to improve the precision of the collocation solutions.

关 键 词：拟Shannon小波 配置解 外推法 两点边值问题 数值解法 

分 类 号：O241.5[理学—计算数学]