TY - JOUR ID - 50382 TI - Non-Standard Finite Difference Schemes for Solving Singular Lane-Emden Equation JO - International Journal of Research in Industrial Engineering JA - RIEJ LA - en SN - 2783-1337 AU - Saberi Najafi, H. AU - Yaghoubi, A. AD - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, Rasht, Iran. AD - Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, University Campus2, Rasht, Iran. Y1 - 2017 PY - 2017 VL - 6 IS - 2 SP - 161 EP - 171 KW - Non-Standard finite difference KW - Lane-Emden equation KW - Astrophysics DO - 10.22105/riej.2017.92303.1001 N2 - In this paper we construct Non-Standard finite difference schemes (NSFD) for numerical solution of nonlinear Lane-Emden type equations which are nonlinear ordinary dierential equations on semi-infinite domain. They are categorized as singular initial value problems. This equation describes a variety of phenomena in theoretical physics and astrophysics.  The presented schemes are obtained by using the Non-Standard finite difference method. The use of NSFD method and its approximations play an important role for the formation of stable numerical methods. The main advantage of the schemes is that the algorithm is very simple and very easy to implement. Thus, this method may be applied as a simple and accurate solver for ODEs and PDEs and it can also be utilized as an accurate algorithm to solve linear and nonlinear equations arising in physics and other fields of applied mathematics. Illustrative examples have been discussed to demonstrate validity and applicability of the technique and the results have been compared with the exact solutions. UR - https://www.riejournal.com/article_50382.html L1 - https://www.riejournal.com/article_50382_48c8abdb20347aa1aecccb32f92c955a.pdf ER -