On the numerical solution of a semilinear elliptic eigenproblem of Lane-Emden type, I: Problem formulation and description of the algorithms

New Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives

In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...

Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method

In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed.

A Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...