基于Legrndre小波的第一类Fredholm积分方程的数值解法研究

Numerical Research of Fredholm Integral Equations of the First Kind Based on the Legendre Wavelets

提出利用Legendre小波函数去获得第一类Fredholm积分方程的数值解,函数定义在区间[0,1)上,然后结合Garlerkin方法将原问题转化为线性代数方程组.而且还对算法的收敛性和误差进行了分析,最后通过两个数值算例验证了所提算法的可行性及有效性.

In this paper, a numerical scheme for solving Fredholm integral equations of the first kind via Legendre wavelet has been proposed, this method is based on the orthogonal functions on[0, 1)combined with Galerkin method, then the original problem is transformed into a system of linear algebraic equations. In addition the convergence and error are investigated. Lastly two numerical examples have been presented to test the effectiveness and feasibility of the proposed method.