The iterated defect correction methods for singular two-point boundary value problems

In this paper, the iterated defect correction (IDeC) techniques based on the centered Euler method for the equivalent first order system of the singular two-point boundary value problem in linear case (x ^α y′(x))′ = f(x), y(0) = a,y(1) = b, where 0 < α < 1 are considered. By using the asymptotic expansion of the global error, it is analyzed that the IDeC methods improved the approximate results by means of IDeC steps and the degree of the interpolating polynomials used. Some numerical examples from the literature are given in illustration of this theory.