A Chelyshkov-based spectral homotopy analysis method for singular nonlinear Lane–Emden-type equations

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Abstract

An enhanced numerical technique for solving the Lane–Emden equation is developed using the spectral homotopy analysis method (SHAM) with Chelyshkov polynomials and Gauss–Lobatto collocation nodes. The numerical results, including absolute errors and comparisons with the exact solution, demonstrate the convergence behavior and accuracy of the proposed approach. The results show that the Chelyshkov-based SHAM provides an effective framework for the numerical treatment of Lane–Emden-type problems.

Keywords

nonlinear equations / Lane–Emden equation / Chelyshkov polynomials / spectral methods / spectral homotopy analysis method

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