Two Efficient Computational Algorithms to Solve the Nonlinear Singular Lane-Emden Equations

Abstract

In this paper, two efficient computational algorithms based on Rational and Exponential Bessel (RB and EB) functions are compared to solve several well-known classes of nonlinear Lane-Emden type models. The problems, which are define in some models of non-Newtonian fluid mechanics and mathematical physics, are nonlinear ordinary differential equations of second-order over the semi-infinite interval and have a singularity at x = 0. The nonlinear Lane-Emden equations are converted to a sequence of linear differential equations by utilizing the quasilinearization method (QLM), and then these linear equations are solved by RB and EB collocation methods. Afterwards, the obtained results are compared with the solution of other methods to demonstrate the efficiency and applicability of the proposed methods.