The exact solution and stability analysis for integral equation of third or first kind with singular kernel

摘要

In this paper, we give representation of exact solution for integral equation of third or first kind with singular kernel by the form of series in the reproducing kernel space. The n-term approximate to the exact solution is obtained by truncating the series and the error is monotone decreasing with increasing item of the n-term approximate solution. The solution is stable in the reproducing kernel space. Some numerical examples are studied to demonstrate the accuracy of the present method.