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.

中文翻译：

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关于在 Lane-Emden 方程上应用的变分迭代方法的说明

目的

在本文中，作者考虑了以下称为 Lane-Emden 方程的非线性奇异边值问题 (SBVP)， − u ″( t )-( α / t ) u ′( t ) =  g ( t , u ), 0 <  t  < 1 其中α  ≥ 1 受两点和三点边界条件的约束。作者建议开发一种新方法来求解 Lane-Emden 方程组。

设计/方法/方法

作者改进了 [JAAC, 9(4) 1242–1260 (2019)] 中提出的修正变异迭代法 (VIM)，大大加快了收敛速度并减少了计算任务。

发现

研究结果表明，可以使用所提出的方法计算 Lane-Emden 方程的精确或高度精确的近似解。

原创性/价值

在 VIM 中进行了新的修改，提供了 Lane-Emden 方程的精确或高度精确的近似解，这在文献中不存在。