Haar Adomian Method for the Solution of Fractional Nonlinear Lane-Emden Type Equations Arising in Astrophysics

Haar wavelet approximate solutions for the generalized Lane-Emden equations arising in astrophysics

This paper provides a technique to investigate the solutions of generalized nonlinear singular Lane–Emden equations of first and second kinds by using a Haar wavelet quasi-linearization approach. The Lane–Emden equation is widely studied and is treated as a challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytr...

Solution of Lane-Emden Type Equations by Combination of the Spectral Method and Adomian Decomposition Method

The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obt...

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...

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the...

Numerical method for solving Lane – Emden type equationsarising in astrophysics