A new pair of block techniques for direct integration of third-order singular IVPs

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-14 DOI:10.1016/j.apnum.2024.06.013

Mufutau Ajani Rufai , Bruno Carpentieri , Higinio Ramos

引用次数: 0

Abstract

This paper proposes a new pair of block techniques (NPBT) for the direct solution of third-order singular initial-value problems (IVPs). The proposed method uses a polynomial and two intermediate points to approximate the theoretical solution of third-order singular IVPs, resulting in a reasonable approximation within the integration interval. The method's essential features, including stability and convergence order, are analyzed. The proposed NPBT method is improved by using an embedding-like strategy that allows it to be executed in a variable step size mode in order to gain better efficiency. The effectiveness of the proposed method is assessed using various model problems. The approximate solution provided by the proposed NPBT method is more accurate than that of the existing methods utilized for comparison. This efficient solution positions NPBT as a good numerical method for integrating third-order singular IVP models in the fields of applied sciences and engineering.

查看原文本刊更多论文

直接积分三阶奇异 IVP 的一对新分块技术

本文提出了一种直接求解三阶奇异初值问题（IVPs）的新型对块技术（NPBT）。所提出的方法使用一个多项式和两个中间点来近似三阶奇异 IVP 的理论解，从而在积分区间内得到合理的近似值。分析了该方法的基本特征，包括稳定性和收敛阶次。通过使用类似嵌入的策略，改进了所提出的 NPBT 方法，使其可以在步长可变的模式下执行，从而获得更好的效率。利用各种模型问题对所提方法的有效性进行了评估。所提出的 NPBT 方法提供的近似解比用于比较的现有方法更精确。这种高效的解法使 NPBT 成为应用科学和工程领域整合三阶奇异 IVP 模型的一种良好数值方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.