A numerical algorithm to solve a class of multi-point boundary value problems

This note presents a numerical algorithm to solve a class of multi-point boundary value problems (MBVPs). Compared to conventional multiple shooting, the proposed method uses less parameters to exploit advantages of single shooting approaches. Unknown parameters are updated by a two-step algorithm which improves the convergence of parameters over existing one-step algorithm. The main idea of the two-step algorithm is to decouple the effects on boundary conditions between two sets of parameters: state and costate, and switch times. The proposed algorithm can compute the solution of a class of MBVPs faster than various existing methods. An application example illustrates the effects of the algorithm.