An analytic algorithm of Lane-Emden-type equations arising in astrophysics - a hybrid approach

Abstract

A new analytic algorithm for Lane-Emden equations is proposed in this paper. The proposed algorithm is obtained by using a new iterative method. The new iterative method is a hybrid of variational iteration method and the Adomian decomposition method and further refined by introducing a new correction functional. This new correction functional is obtained from the standard correction functional of variational iteration method by introducing an auxiliary parameter γ in it. Further, a sequence G n x , with suitably chosen support, is also introduced in the new correction functional. The algorithm is easy to implement and gives fairly accurate solutions. Several test examples are given establishing the accuracy and the efficiency of the algorithm.

Higher order numeric solutions of the Lane–Emden-type equations derived from the multi-stage modified Adomian decomposition method

“…Consider the well-known white-dwarf equation [2,3,6,26] with a quadratic and fractional-power nonlinearity…”

Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane–Emden type differential equations (LETDEs)

“…These types of equations generally occur in the principle of stellar structure, the thermal behaviour of a spherical bunch of gas, isothermal gas spheres (IGSs) and the principle of thermionic currents (Richardson 1921 ; Chandrasekhar 1967 ; Davis 1962 ).…”

“…Two astrophysicists, Jonathan Homer Lane and Robert had explained the Lane–Emden type differential equations. In this study, they had designed these types of differential equations, which is a dimensionless structure of Poisson’s equation for the gravitational potential of a self-gravitating, spherically symmetric, polytropic fluid and the thermal behavior of a spherical bunch of gas according to the laws of thermodynamics (Lane 1870 ; Richardson 1921 ). The Lane–Emden type of differential equation is also called the polytropic differential equations and it is given by: where is a dimensionless radius and is linked to the density (and accordingly the pressure) by for central density .…”

Application of the homotopy perturbation method for solving fractional Lane-Emden type equation

“…Many problems in mathematical physics can be modelled by the so-called initial value problems of Lane-Emden type equation [1][2][3][4][5] where A is a constant and f(y) is a given function of y. Equation (1) usually arises in the study of thermal physics, fluid mechanics, relativistic mechanics, population evolution and the chemical reactor systems [6][7][8][9][10][11][12].…”