A note on variation iteration method with an application on Lane–Emden equations. Issue 10 (25th May 2021) - Verma, Amit K.; Kumar, Narendra; Singh, Mandeep; Agarwal, Ravi P.
Abstract : Purpose: In this article, the authors consider the following nonlinear singular boundary value problem (SBVP) known as Lane–Emden equations, − u ″( t )-( α / t ) u ′( t ) =  g ( t, u ), 0 <  t  < 1 where α  ≥ 1 subject to two-point and three-point boundary conditions. The authors propose to develop a novel method to solve the class of Lane–Emden equations. Design/methodology/approach: The authors improve the modified variation iteration method (VIM) proposed in [JAAC, 9(4) 1242–1260 (2019)], which greatly accelerates the convergence and reduces the computational task. Findings: The findings revealed that either exact or highly accurate approximate solutions of Lane–Emden equations can be computed with the proposed method. Originality/value: Novel modification is made in the VIM that provides either exact or highly accurate approximate solutions of Lane-Emden equations, which does not exist in the literature.