# AN EFFECTIVE NUMERICAL METHOD FOR SOLVING THE NONLINEAR SINGULAR LANE-EMDEN TYPE EQUATIONS OF VARIOUS ORDERS

## DOI:

https://doi.org/10.11113/jt.v79.8737## Keywords:

Fractional order of the Chebyshev functions, Lane-Emden type equations, Isothermal gas sphere equation, Collocation method, Nonlinear ODE## Abstract

The Lane-Emden type equations are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. These equations are categorized as non-linear singular ordinary differential equations on the semi-infinite domain. In this paper, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind have been introduced as a new basis for Spectral methods, and also presented an effective numerical method based on the GFCFs and the collocation method for solving the nonlinear singular Lane-Emden type equations of various orders. Obtained results have compared with other results to verify the accuracy and efficiency of the presented method.

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*79*(1). https://doi.org/10.11113/jt.v79.8737