The Numerical Method for Solving Differential Equations of Lane-Emden Type by Padé Approximation

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...

Numerical method for solving Lane – Emden type equationsarising in astrophysics

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 ...

Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation

Lane-Emden differential equations of order fractional has been studied. Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.

Rational Chebyshev Collocation Method for Solving Nonlinear Ordinary Differential Equations of Lane-emden Type

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...