Solving certain classes of Lane-Emden type equations using the differential transformation method

Abstract

Abstract In this paper, the differential transformation method (DTM) is applied to solve singular initial problems represented by certain classes of Lane-Emden type equations. Some new differential transformation formulas for certain exponential and logarithmic nonlinearities are derived. The approximate and exact solutions of these equations are calculated in the form of series with easily computable terms. The results obtained with the proposed methods are in good agreement with those obtained by other methods. The advantages of this technique are shown as well.