Convergence analysis of a numerical method to solve the adjoint linearized periodic orbit equations (Q1957193)

The authors deal with the equation adjoint to the linearization of the periodic orbit equations in a dynamical system. Some numerical methods were already introduced in literature to solve the adjoint equations. Among them, a recent approach was presented for the computation of the solution as a byproduct of the computation of the periodic orbit. However, this method was lacking in a rigorous convergence analysis, which, instead, is the aim of this remarkable paper. Actually, the method is analyzed in detail and proved to be equivalent to a collocation method for the adjoint equations and consequently its convergence and order of convergence are obtained. The paper enjoys some significant detailed numerical examples. Unfortunately, the announced Section 4 devoted to some conclusions is not present.