Abstract:A collocation method is introduced for a class of Fredholm integral equation of its first kind with weakly singular kernels. The key idea of this method is splitting the weakly singular kernel of the integral operator into finite parts so that the weak singularity is concentrated on one which can be analytically solved using integration by parts. Theoretical analysis and numerical examples show this method can achieve accuracy O(h ^m+1), with h being the step size, and the highest order of the basis function.