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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., Comment: 21 pages. arXiv admin note: text overlap with arXiv:1606.07615

The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted Bessel polynomials on the interval [a, b] are calculated. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ODE to the solution of a system of algebraic equations with unknown Bessel coefficients. The comparisons between the results of the present work and other the numerical method are shown that the present work is computationally simple and highly accurate., Comment: 23 pages