A note on variation iteration method with an application on Lane–Emden equations
2021; Emerald Publishing Limited; Volume: 38; Issue: 10 Linguagem: Inglês
10.1108/ec-10-2020-0604
ISSN1758-7077
AutoresAmit K. Verma, Narendra Kumar, Mandeep Singh, Ravi P. Agarwal,
Tópico(s)Nonlinear Waves and Solitons
ResumoPurpose 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.
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