积分方程的Legendre多小波自适应解法

摘要

由多分辨分析理论,构造了L2([0,1])上的分段Legendre多小波基函数,并利用所构造的基函数提出了求解积分方程的配点法.求解过程中,对小波系数用阈值进行筛选,利用分段Legendre多小波基函数求解.以第一类Fredholm积分方程为例,表明该算法简单有效.%By multi-resolution analysis theory,the piecewise Legendre multi-wavelets basis function on L2([0,1]) was constructed,and the basis functions were used for solving integral equations by collocation method.In the solving process,the threshold value of wavelet coefficient was screened,using piecewise Legendre multi-wavelet basis function to solve.In the first category Fredholm integral equation,for example,shows that the algorithm is simple and effective.