Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems Original Research Article

Iterated deferred correction algorithms, based on special classes of implicit Runge-Kutta formulae, have proved to be a very effective way of solving general first order systems of nonlinear two-point boundary value problems. Since this is essentially a finite difference approach it suffers from the usual disadvantage in that accurate solutions are provided only at the mesh points rather than over the whole range of integration. In this paper we investigate the problem of deriving interpolating polynomials which are able to provide a continuous solution with a uniform accuracy comparable to that obtained at the mesh points. Interpolants of various orders are derived for the code TWPBVP, which is based on MIRK formulae, and for ACDC which is based on Lobatto formulae with continuation. Both of these codes are freely available from NETLIB. The quality of the interpolants derived for these two codes is illustrated by numerical examples.