An efficient computational technique to solve second order Lane-Emden-Fowler type equations arising in physical phenomena

Abstract This article focuses on finding numerical solutions of high accuracy and low computational cost for second order Lane-Emden-Fowler type equations. The significance of these nonlinear equations is rooted in their ability to model important physical, astrophysical, and biological phenomena. The proposed study uses cubic spline approximations for discretization along with half-step grid points to develop a fourth order implicit numerical method capable of solving highly non-linear and singular equations with high accuracy. A comprehensive convergence analysis shows the claimed fourth order convergence of the scheme which is confirmed by graphical and computational results found for seven test problems involving various initial and boundary conditions.