Numerical solution of Bratu’s boundary value problem based on Green’s function and a novel iterative scheme

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-23 DOI:10.1186/s13661-023-01791-6

Junaid Ahmad, Muhammad Arshad, Kifayat Ullah, Zhenhua Ma

引用次数: 0

Abstract

Abstract We compute the numerical solution of the Bratu’s boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green’s function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu’s BVP. Furthermore, we show that the suggested new iterative scheme is essentially weak $w^{2}$ w 2 -stable in this setting. We perform some numerical computations and compare our findings with some other iterative schemes of the literature. Numerical results show that our new approach is numerically highly accurate and stable with respect to different set of parameters.

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基于格林函数和一种新的迭代格式的Bratu边值问题的数值解

摘要计算了Banach空间上Bratu边值问题的数值解。为此，我们将格林函数嵌入到一个新的两步迭代方案中。然后，在一定的假设条件下，我们证明了这种新的迭代格式收敛于一维非线性Bratu’s BVP的求解。进一步，我们证明了所建议的新迭代格式本质上是弱$w^{2}$ w 2 -稳定的。我们进行了一些数值计算，并将我们的发现与文献中其他一些迭代格式进行了比较。数值结果表明，该方法具有较高的数值精度和稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.