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.

中文翻译：

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求解非线性奇异Lane-Emden方程的两种高效计算算法

在本文中，比较了两种基于有理和指数贝塞尔（RB 和 EB）函数的高效计算算法，以解决几个著名的非线性 Lane-Emden 类型模型。在非牛顿流体力学和数学物理的一些模型中定义的问题是半无限区间上的二阶非线性常微分方程，并且在 x = 0 处具有奇点。 非线性 Lane-Emden 方程为利用拟线性化方法（QLM）将线性微分方程转化为一系列线性微分方程，然后通过RB和EB搭配方法求解这些线性方程。然后，将所得结果与其他方法的解决方案进行比较，以证明所提出方法的有效性和适用性。