Error estimates for parallel shooting using initial or boundary value methods Original Research Article

In the first part of this work (Sections 2 and 3) we derive from previous papers an outline of a general method to estimate the global discretization error in the numerical solution of a linear boundary value problem when the parallel shooting technique is used. Then, in Sections 4 and 5, the proposed error estimation is shown to be well suited in the case that the involved initial value problems are solved either by traditional linear k-step initial value methods or by boundary value methods. As the estimated error follows carefully the behaviour of the true error it can be used to improve the numerical solution as shown in some numerical examples.