  We develop a "hybrid approximative scheme" in the framework of the
post-Newtonian approximation for computing general-relativistic polytropic
models simulating neutron stars in critical rigid rotation. We treat the
differential equations governing such a model as a "complex initial value
problem", and we solve it by using the so-called "complex-plane strategy". We
incorporate into the computations the complete solution for the relativistic
effects, this issue representing a significant improvement with regard to the
classical post-Newtonian approximation, as verified by extended comparisons of
the numerical results.
