Using Reproducing Kernel for Solving‎ ‎the Lane-Emden Equations‎, ‎Arising in Astrophysics

Subject Areas : International Journal of Mathematical Modelling & Computations

Ebrahim Amini ^{1 *} , Asghar Taheri ² , Majid Abedini ³

1 - Department of Mathematics, Payme Noor University, P. O. Box 19395-4697, Tehran, IRAN
2 - Department of Mathematics, Payme Noor University.
3 - Department of Mathematics, Payme Noor University

Received: 2020-04-10 Accepted : 2020-06-20 Published : 2020-09-01

Keywords: Lane-Emden equation, Reproducing kernel Hilbert space method, astrophysics equation‎,

Abstract :

‎In this paper‎, ‎we utilize an algorithm for solving nonlinear ordinary differential equations of Lane-Emden type on a semi-infinite interval‎. ‎The algorithm is based on an iterative technique and the‎reproducing kernel Hibert method‎. ‎We give‎ the convergence analysis for the proposed method‎. ‎The validity and applicability of the proposed‎ ‎method are demonstrated by some numerical examples‎. ‎The obtained results and comparison with‎ ‎other methods provide confirmation for the validity of our numerical method‎.