Solution of Lane–Emden type equations using Bernstein operational matrix of differentiation

The purpose of this paper is to propose an efficient numerical method for solving Lane–Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane–Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.

► We constructed the Bernstein operational matrix of differentiation.
► Lane–Emden equations have been solved using the constructed operational matrix of differentiation.
► Only small size operational matrix is required to provide the solution at high accuracy.