Solving Lane-Emden equation using Pad´E approximation method / Najir Tokachil ... [et al.]

The Lane-Emden equations are singular initial value problems associated with ordinary differential equations of the second order (ODEs), (Zhou, 1986). The equations have been used to model a variety of mathematical physics and astrophysics phenomena. The equation is essential in mathematical physics, celestial mechanics, and computer science. Various approximations have been used to solve multiple variations of the Lane-Emden problem: Legendre Wavelets Approximations, Hybrid Adomian Decomposition, Method-Successive Linearization Method (ADM-SLM), q-homotopy analysis, Laplace transform method (q-HATM), and others. However, not all solutions to the Lane-Emden equation are accurate. In this study, an example of the Lane-Emden equation is solved using Pade’s approximation method, and the result will be compared with the exact and Taylor’s series solutions.