Representation of the exact solution and a stability analysis on the Fredholm integral equation of the first kind in reproducing kernel space

In this paper, a new method is given in order to solve an ill-posed problem on Fredholm integral equation of the first kind. The representation of the exact solution is given and the stability of the solution on Fredholm integral equation of the first kind is discussed in the reproducing kernel space. By the discussions, a conclusion is obtained the stability problem is a well-posed problem in the reproducing kernel space, namely, the measurement errors of the experimental data can not result in unbounded errors of the exact solution. The numerical experiment shows that the new method given in the paper is valid.