Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta form ulae is developed for the efficient numerical solution of nonlinear stiff t wo-point boundary value problems. An analysis of the stability properties o f general deferred correction schemes which are based on implicit Runge-Kut ta methods is given and results which are analogous to those obtained for i nitial value problems are derived. A revised definition of symmetry is pres ented and this ensures that each deferred correction produces an optimal in crease in order. Finally, some numerical results are given to demonstrate t he superior performance of Lobatto formulae compared with mono-implicit for mulae on stiff two-point boundary value problems. (C) 1998 Elsevier Science Ltd. All rights reserved.