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A note on variation iteration method with an application on Lane–Emden equations

Amit K. Verma (Department of Mathematics, Indian Institute of Technology Patna, Patna, India)
Narendra Kumar (Department of Mathematics, Indian Institute of Technology Patna, Patna, India)
Mandeep Singh (Department of Mathematics, JUIT, Waknaghat, India)
Ravi P. Agarwal (Department of Mathematics, Texas A&M University Kingsville, Kingsville, Texas, USA)

Engineering Computations

ISSN: 0264-4401

Article publication date: 25 May 2021

Issue publication date: 7 December 2021

275

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

Copyright © 2021, Emerald Publishing Limited

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