A Collocation Method for Weakly Singular Fredholm Integral Equation

A collocation method is introduced for a class of Fredholm integral equation of the second 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 in one which can be analytically solved using integration by parts. Theoretical analysis and numerical examples show that this method can achieve accuracy O(h^m+1), and this accuracy will not reduce when α → 1.