A Deep-Learning-Based Method for Solving Nonlinear Singular Lane-Emden Type Equation

Generalized Laguerre Polynomials Collocation Method for Solving Lane-Emden Equation

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...

a parametric iteration method for solving lane-emden type equations

in this paper, an analytical method called the parametric iteration method (pim) is presented for solving the second-order singular ivps of lane-emden type, and its local convergence is discussed. since it is often useful to have an approximate analytical solution to describe the lane-emden type equa- tions, especially for ones where the closed-form solutions do not exist at all, therefore, an ...

Ultraspherical Wavelets Method for Solving Lane-emden Type Equations

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

Lane-Emden Equation: perturbation method

The perturbation method is applied to numerical solution of the Lane-Emden Equation (LEE)of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.

Numerical method for solving Lane – Emden type equationsarising in astrophysics