基于Haar小波求解第二类Fredholm积分方程

摘要

The solution of the second kind Fredholm integral equation based on the Haar wavelet is studied. The Haar wavelet family is given. The Haar integral operations is established, functions are utilized as a basis to convert the second kind Fredholm integral equation into a system of linear equations. The accurate numerical solution of integral equation is obtained by the Matlab simulation. The numerical solution of integral equations with exact solutions are compared, the result shows that the algorithm is high accuracy.%给出Haar小波族,函数逼近并建立Haar积分算子矩阵,该矩阵将积分运算转化为矩阵运算.采用Haar小波函数基作为基底,将积分方程转换为代数方程组求解.通过Matlab模拟获取数值解,并与积分方程的精确解进行比较,表明该算法具有较高的精确度.