On the rate of convergence of the quasi-linearization method

It is well known that the method of quasi-linearization is quadratically convergent for nonlinear two-point boundary value and system identification problems. In order to avoid the storage of successive approximations, it is sometimes convenient to integrate the original differential equations instead of storing the solution of the linearized equations. This reduces the rate of convergence, but it is generally not known by how much. It is shown that even for the simplist problem, the penalty in increased computing time can be dramatic.