Global error estimates for the standard parallel shooting method

摘要

We present an a posteriori procedure for estimating the global discretization error in the numerical solution of a boundary value problem for a system of m first-order ordinary differential equations, when the parallel shooting algorithms is used. Both nonlinear and linear systems are considered and expressions of the corresponding global discretization error are given, showing slight formal differences between the two cases. As shooting reduces boundary value problems to initial-value problems, an error estimation for a boundary value problem is obtained assuming that an error estimation procedure for initial-value problems is available. However, the number of initial-value problems to be considered in the present error estimation is sharply reduced with respect to the number of initial-value problems proposed by the shooting method.