A WAVELET METHOD FOR THE FREDHOLMINTEGRO-DIFFERENTIAL EQUATIONS WITH CONVOLUTION KERNEL

作     者：Xiao-qing Jin Vai-Kuong Sin(Faculty of Science and Technology, University of Macao, Macao)Jin-yun Yuan(Department of Mathematics, Universidade Federal do Parana, Curitiba, Brazil) 

作者机构：澳门大学科技学院 澳门 Universidade Federal do Parana 巴西 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：1999年第17卷第4期

页      面：435-440页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：Fredholm integro-differential equation Kernel Wavelet transform,Toeplitz matrix Hankel matrix Sobolev spaceg PCG method. 

摘      要：We study the Fredholm integro-differential equationby the wavelet method. Here (x) is the unknown function to be found, k(y) isa convolution kernel and g(x) is a given function. Following the idea in [7], theequation is discretized with respect to two different wavelet bases. We then havetwo different linear systems. One of them is a Toeplitz-Hankel system of the form(Hn + Tn)x = b where Tn is a Toeplitz matrix and Hn is a Hankel matrix. Theother one is a system (Bn+ Cn)y= d with condition number K = O(1) after adiagonal scaling. By using the preconditioned conjugate gradient (PCG) methodwith the fast wavelet transform (FWT) and the fast iterative Toeplitz solver, wecan solve the systems in O(nlog n) operations.