On the order of deferred correction

New deferred correction methods for the numerical solution of initial value problems in ordinary differential equations have recently been introduced by Dutt, Greengard and Rokhlin. A convergence proof is presented for these methods, based on the abstract Stetter–Lindberg–Skeel framework and Spijker-type norms. It is shown that p corrections of an order-r one-step solver yield order-r(p+1) accuracy.