Consider a linear operator equation \(x - Kx = f,\) where f is given and K is a Fredholm integral operator with a Green’s function type kernel defined on C[0, 1]. For \(r \ge 0,\) we employ the interpolatory projection at \(2r + 1\) collocation points (not necessarily Gauss points) onto a space of piecewise polynomials of degree \(\le 2r\) with respect to a uniform partition of [0, 1]. Previous researchers have established that the iterations in the collocation method and its variants improve the orders of convergence by projection methods in the case of smooth kernels. In this article, we demonstrate the improvement in order of convergence by iterated versions of collocation and modified collocation methods when the kernel is of Green’s function type.
