Purpose

The purpose of this study is to implement a newly introduced numerical scheme for the numerical solution of a class of nonlinear fractional Bratu-type boundary value problems (BVPs).

Design/methodology/approach

This strategy is based on a generalization of the variational iteration method (VIM). This proposed generalized VIM (GVIM) is particularly suitable for tackling BVPs.

Findings

This scheme yields accurate solutions for a class of nonlinear fractional Bratu-type BVPs, for which the errors are uniformly distributed across a given domain. A proof of convergence is included. The numerical results confirm that this approach overcomes the deficiency of the VIM and other methods that exist in the literature in the sense that the solution does not deteriorate as the authors move away from the initial starting point.

Originality/value

The method introduced is based on original research that produces new knowledge. To the best of the authors’ knowledge, this is the first time that this GVIM is applied to fractional BVPs.

中文翻译：

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分数Bratu型BVP的数值解：广义变分迭代方法

目的

这项研究的目的是为一类非线性分数阶Bratu型边值问题（BVPs）的数值解实现新引入的数值方案。

设计/方法/方法

该策略基于变分迭代方法（VIM）的概括。提议的通用VIM（GVIM）特别适合处理BVP。

发现

该方案为一类非线性分数Bratu型BVP提供了精确的解决方案，其误差在给定域中均匀分布。包含收敛证明。数值结果证实，该方法克服了VIM和文献中存在的其他方法的不足，从某种意义上说，解决方案不会随着作者远离初始起点而恶化。

创意/价值

引入的方法基于产生新知识的原始研究。据作者所知，这是第一次将此GVIM应用于分数BVP。