An efficient computational approach to solving singular initial value problems for Lane–Emden type equations

• The general differential transformation formula is proved.
• The general formula is presented for any analytic nonlinear terms.
• No discretization, linearization or perturbation is required.
• Nonlinear differential equations are solved using the proposed formula.

In the paper, we present the new computational approach for solving singular initial problems for the Lane–Emden type equations with nonlinear terms based on the differential transformation method (DTM) and the modified general formula for the Adomian polynomials with differential transformation components. To illustrate the capability and efficiency of the method three examples are given. The results obtained in this work are also compared with numerical results of Heydari et al. (2012), Wazwaz (2005), Singh et al. (2009) and the standard DTM as well. These results show that the proposed technique, without linearization or small perturbation, is very effective and convenient for solving of linear and nonlinear differential equations.