基于有理Haar小波求解分数阶第2类Fredholm积分方程

Numerical Solution of Fractional Fredhlom Integral Equation of the Second Kind Based on the Rationalized Haar Wavelet

利用有理Haar小波函数数值求解分数阶第2类Fredholm积分方程,用有理Haar小波定义及性质与配置法给出有理Haar小波积分算子矩阵,将积分方程转化为代数方程组进行求解.最后通过误差分析和数值算例将分数阶积分方程的精确解和用Haar小波所得数值解进行比较,表明了该算法具有较高的精确度.

The rationalized Haar functions are used to solve the solution of fractional order Fredholm integrat equa- tion of the second kind. The integral equation can be reduced to a system of algebraic equations by using ration- ahzed Haar wavelet and collection method. Finally,the numerical solution of fractional integral equation with exact solution and the numerical solutions using Haar wavelet are compared by error analysis and numerial examples. The result shows that the algorithm has high accuracy.