Exact Solutions of Singular IVPs Lane-Emden Equation

Document Type: Original Article

Author

Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran

Abstract

In the paper, [A.M. Rismani, H. Monfared, Numerical solution of singular ivps of laneemden type using a modifi ed Legendre spectral method. Applied Mathematical Modelling, 36 (2012), 4830-4836.], the authors state that exact solutions for the Lane-Emden nonlinear differential equation exist only for m = 0,1 (linear cases) and 5 (nonlinear case). While here,
we present real exact solutions for m ∈ (3,∞) and complex m ∈ (−∞,3){1}. Some illustrated
examples presented as well.

Keywords


[1]A.M. Rismani, H. Monfared, Numerical solution of singular ivps of laneemden type using a modifi ed legendrespectral
method. Applied Mathematical Modelling, 36 (2012), 4830-4836.


[2]Y. Khan, Z. Svoboda, Z.Smarda, Solving certain classes of Lane-Emden type equations using the differential
transformation method. Advances in Difference Equations, 2012(1) (2012), 174. doi:10.1186/1687-1847-2012-174.

[3]S. Liao, A new analytic algorithm of laneemden type equations. Applied Mathematics and Computation, 142(1)
(2003), 1-16. doi:10.1016/S0096-3003(02)00943-8.


[4]A. Yldrm, T. OZiS. , Solutions of singular ivps of laneemden type by homotopy perturbation method. Physics Letters
A, 369(1) (2007), 70-76. doi:10.1016/j.physleta.2007.04.072.


[5]C.M. Bender, K.A. Milton, S.S. Pinsky, L.M. Simmons, A new perturbative approach to nonlinear problems.
Journal of Mathematical Physics, 30(7), (1989) 1447-1455.