The method of successive extrapolated iterated defect correction and its application to second kind Fredholm's integral equations

We describe an application of the principle of Iterated Defect Correction (IDeC) on the quadrature methods for the numerical solution of Fredholm's integral equations of the second kind. We also derive an asymptotic expansion for the global error in the solution produced by the IDeC method. Applying Richardson extrapolation repeatedly on the IDeC method, we present the technique of Successive Extrapolated Iterated Defect Correction (SEIDeC) and the resulting asymptotic expansion for the global error. Numerical tests confirm the asymptotic results and demonstrate the power of the IDeC method as well as the superiority of our method SEIDeC.