A note on variation iteration method with an application on Lane–Emden equations
ISSN: 0264-4401
Article publication date: 25 May 2021
Issue publication date: 7 December 2021
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.
Keywords
Acknowledgements
The authors are thankful to anonymous reviewers for their valuable comments that have helped them a lot in improving the paper.
Citation
Verma, A.K., Kumar, N., Singh, M. and Agarwal, R.P. (2021), "A note on variation iteration method with an application on Lane–Emden equations", Engineering Computations, Vol. 38 No. 10, pp. 3932-3943. https://doi.org/10.1108/EC-10-2020-0604
Publisher
:Emerald Publishing Limited
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