积分方程的Legendre多小波自适应解法

由多分辨分析理论,构造了L(20,1])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.

Legendre Multi-wavelets Adaptive Method for Integral Equations

By multi-resolution analysis theory,the piecewise Legendre multi-wavelets basis function on L2() 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.