  In this paper, we decide to compare two new approaches based on Rational and
Exponential Bessel functions (RBs and EBs) to solve several well-known class of
Lane-Emden type models. The problems, which define in some models of
non-Newtonian fluid mechanics and mathematical physics, are nonlinear ordinary
differential equations of second-order over the semiinfinite interval and have
singularity at x = 0. We have converted the nonlinear Lane-Emden equation to a
sequence of linear equations by utilizing the quasilinearization method (QLM)
and then, these linear equations have been solved by RBs and EBs
collocation-spectral methods. Afterward, the obtained results are compared with
the solution of other methods for demonstrating the efficiency and
applicability of the proposed methods.
