第一类弱奇异核Fredholm积分方程的数值求解

A Numerical Solution of Weakly Singular Fredholm Integral Equation of First Kind

第一类弱奇异核Fredholm积分方程由于奇异及本质的不适定性,给求解带来很大难度.本文首先利用克雷斯变换将方程转化,并对转化后的方程进行高斯-勒让德离散,得到一离散不适定的线性方程组,结合正则化方法对该类问题进行数值求解。最后给出了数值模拟,验证了本文方法的可行性及有效性.

Beacause the weakly singular Fredholm integral equation of first kind the nature of the singularity and ill-posedness, so solving is great difficulty. Then we firstly transform the equation into by Kress, and ransformed equations and Gauss-Legendre discrete, and we get the not be a discrete set of linear equations. Regularization method with the class of the numerical solution of the problem. Finally, a numerical simulation verify the feasibility and effectiveness.