To check the applicability of OHAM for TPBVP, in this section four examples of TPBVP are presented in which one example is linear and the remaining are nonlinear.
This paper reveals that OHAM is a very strong method for solving TPBVP and gives us a more accurate solution as compared to other methods.
We still need to solve the TPBVPs  when adopting above modification algorithm.
Equations (20)~(21) satisfy initial conditions [delta]x([t.sub.0]) = [delta][x.sub.0], [delta][lambda]([t.sub.0]) = [delta][[lambda].sub.0] and terminal conditions (13)~(15) form the TPBVPs of [delta]x, [delta][lambda].
This generates a number of approximately shortest path segments defined by solving a TPBVP for the geodesic differential equations between two consecutive path points.
We mention that in general a closed-form solution to TPBVP for the geodesic differential equations is not available, or the derivation of geodesic differential equations is nearly impossible, so that the geodesic can only be numerically defined.
Thus, the low-thrust optimal trajectory design can be converted into a TPBVP
, which consists in finding the unknown initial costate vector.