A numerical approach for solving singular nonlinear Lane–Emden type equations arising in astrophysics

• To present an efficient method to solve Lane–Emden type equations.
• To represent smooth and especially piecewise smooth functions properly.
• To improve the accuracy by properly increasing either the number of subintervals or the number of collocation points.
• To compare present solutions for more accuracy and efficiency.

In this paper, we suggest a numerical method based upon hybrid of Chebyshev wavelets and finite difference methods for solving well-known nonlinear initial-value problems of Lane–Emden type. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of nonlinear algebraic equations. Making a comparison among the obtained results using the present method with those ones reported in literature by some other well-known methods confirms the accuracy and computational efficiency of the present technique.