Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic R-n behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a(0) using a minimal number of grid points. Calculations with two electronic states, A (1)Sigma(u)(+) and b (3)Pi(u) states, both correlated to the Rb(5s) + Rb(5p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb-2(0(u)(+)) spectrum, manifested under the 5s, 5p P-2(1/2) dissociation limit by an oscillatory behavior of the rotational constants.