Two efficient computational algorithms to solve the singularly perturbed Lane-Emden problem
This work provides alternative numerical solutions for a class of nonlinear differential equations in fluid mechanics and physics, but the improvement is incremental.
The paper introduces two computational methods using Rational and Exponential Bessel functions to solve singularly perturbed Lane-Emden equations, demonstrating efficiency through comparisons with existing methods.
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.