Solution for the System of Lane–Emden Type Equations Using Chebyshev Polynomials

Yalçın Öztürk
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Yalçın Öztürk: Ula Ali Koçman Vocational High School, Muğla Sıtkı Koçman University, Muğla 48000, Turkey

Mathematics, 2018, vol. 6, issue 10, 1-13

Abstract: In this paper, we use the collocation method together with Chebyshev polynomials to solve system of Lane–Emden type (SLE) equations. We first transform the given SLE equation to a matrix equation by means of a truncated Chebyshev series with unknown coefficients. Then, the numerical method reduces each SLE equation to a nonlinear system of algebraic equations. The solution of this matrix equation yields the unknown coefficients of the solution function. Hence, an approximate solution is obtained by means of a truncated Chebyshev series. Also, to show the applicability, usefulness, and accuracy of the method, some examples are solved numerically and the errors of the solutions are compared with existing solutions.

Keywords: system of Lane-Emden; engineering problem; Chebyshev polynomials; L 2 error (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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