On the order of deferred correction

Abstract

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.