摘要
为了求解数值积分,利用第2类Chebyshev小波函数构造了一些求解定积分的数值积分公式。该算法的主要思想是将被积函数利用小波基函数的线性组合来进行表达,通过离散化被积分函数得到相应的Chebyshev小波矩阵,再通过小波基函数在[0,1]区间上的积分得到了求积系数。通过第2类Chebyshev多项式的解析表达式,推导了Chebyshev小波基函数的一般积分公式,从而为该小波的应用提供了方便。通过大量数值实例验证了该方法的可行性及有效性。该算法编程简单,应用方便,也适用于奇异积分、震荡函数积分问题。
In order to solve numerical integration,the second kind Chebyshev wavelets are applied to construct some numerical integral formulas. The main idea of this method is that the integrands are expressed by the second kind Chebyshev wavelets and the corresponding Chebyshev wavelets matrix is obtained by discretizing the integrand. Quadrature coefficients are calculated by combining the Chebyshev wavelets matrix and the integral of the wavelet basis function on the interval [ 0,1 ]. Ac- cording to the analytic expression of Chebyshev polynomial of the second kind, the general integral formula of the Chebyshev wavelets function is deduced ,which is convenient for the application of the second kind Chebyshev wavelets. The feasibility and effectiveness of the method are verified by some numerical examples. The algorithm is simple and easy to implement. It is also applicable to singular integral and oscillating function integral problems.
作者
刘智政
吴金良
杨宙
许小勇
LIU Zhizheng;WU Jinliang;YANG Zhou;XU Xiaoyong(School of Science,East China University of Technology,330013,Nanchang,PRC)
出处
《江西科学》
2018年第6期954-960,共7页
Jiangxi Science
基金
国家自然科学基金项目(No.11601076)
江西省教育厅科学技术研究项目(GJJ170473)
东华理工大学第十四届大学生科技创新基金项目
