Solving the Lane–Emden equation by using Bernstein operational matrix

Lane–Emden equations model a wide range of problems in physics and astrophysics, with applications including stellar structure, radiative cooling, and the modeling of galaxy clusters. This study proposes an efficient numerical method to solve the Lane–Emden equation using Bernstein polynomials. By deriving the Bernstein Operational Matrix of Derivative, it can be applied to solve linear Lane–Emden type Ordinary Differential Equations. Various types of collocation points are being used in this study to determine which collocation points have the highest efficiency. The method’s efficiency has also been determined by calculating the infinity norm of the absolute errors at the collocation points. Several illustrative examples are provided to demonstrate the efficiency and validity of the method.