A discrete method of accuracy O(hm) is constructed to solve the integral equation eigenvalue problem λϕ(x)=∫−11K(x,y)ϕ(y)dy, where K(x, y)=log|x−y| or K(x, y)=|x−y|−α, 0α1, ϕ(x) being the eigenfunction associated with the eigenvalue λ. The method is based first on improving the...