Superconvergent deferred correction methods or first order systems of nonlinear two-point boundary value problems

Iterated deferred correction is a widely used approach to the numerical sol ution of rst order systems of nonlinear two-point boundary value problems. Normally the orders of accuracy of the various methods used in a deferred c orrection scheme di er by 2, and, as a direct result, each time a deferred correction is applied the order of the overall scheme is increased by a max imum of 2. In this paper we consider the construction of mono-implicit Rung e Kutta ( MIRK) methods where an increase of four orders of accuracy is obt ained for each deferred correction. We develop a very powerful yet rather s traightforward theory which allows us to identify the appropriate Runge Kut ta formulae for inclusion in such schemes. In particular, we will focus on the construction of pairs of MIRK formulae of order 4 and 8 which will allo w this superconvergence to be realized. We will further show that it is pos sible to derive formulae of this type for which high order interpolants and accurate error estimates are readily available.