Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane-Emden type differential equations (LETDEs).
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP 473226 India.
Rajnee
R
Tripathi
Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP 473226 India.
Hradyesh Kumar
HK
Mishra
Homotopy Perturbation Method (HPM); Lane–Emden type equations; Laplace Transform (LT); Singular Initial value problems (IVPs)