We find a numerical self-consistent stellar model by finding the distribution
function of a thin disk that satisfies simultaneously the Fokker-Planck and
Poisson equations. The solution of the Fokker-Planck equation is found by a
direct numerical solver using finite differences and a variation of Stone's
method. The collision term in the Fokker-Planck equation is found using the
local approximation and the Rosenbluth potentials. The resulting diffusion
coefficients are explicitly evaluated using a Maxwellian distribution for the
field stars. As a paradigmatic example, we apply the numerical formalism to
find the distribution function of a Kuzmin-Toomre thin disk. This example is
studied in some detail showing that the method applies to a large family of
actual galaxies.Comment: 12 pages, 9 figures, version accepted in Astronomy & Astrophysic
