Legendre多小波方法求解第一类Fredholm积分方程

Legendre Multi-wavelets Adaptive Method for First Category Fredholm Integral Equations

根据小波分析的多分辨分析理论,构造了L2([0,1])上的分段Legendre多小波基函数,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 structure of piecewise Legendre multi wavelets basis function on L2（[0, 1]）, and the basis functions were used for solving integral equations by collocation method. In the solving process, the wavelet coefficient with threshold value selection, using piecewise Legendre many wavelet basis function to solve. In the first category Fredholm integral equation, for exam- ple, shows that the algorithm is simple and effective.