An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order

Abstract

The Lane-Emden type equations of arbitrary (fractional and integer) order and the white dwarf equation are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. In this paper, an efficient numerical algorithm based on the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) and the collocation method to solve these well-known differential equations is presented. The operational matrices of the fractional derivative and the product of order $\alpha$ in the Caputo's definition for the GFCFs are used. The obtained results are compared with other results to verify the accuracy and efficiency of the presented method. The obtained numerical results are better than other proposed methods.

Keywords

• fractional order of the Chebyshev functions,Lane-Emden type equations,operational matrix,Tau-Collocation method,white dwarf equation

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