文章基本信息

标题：Direct Solution of u ″ = f ( t , u , u ′ ) Using Three Point Block Method of Order Eight with Applications
本地全文：下载
作者：Reem Allogmany ; Fudziah Ismail
期刊名称：Journal of King Saud University - Science
印刷版ISSN：1018-3647
出版年度：2021
卷号：33
期号：2
页码：1-8
DOI：10.1016/j.jksus.2020.101337
语种：English
出版社：Elsevier
摘要：AbstractThis study aims to construct an implicit block method with three-point to tackle general second-order ordinary differential equations (ODEs) directly. Hermite Interpolating Polynomial is used as the fundamental function to obtain the proposed method which involved the first and second derivatives off(t,u,u′). From the investigation done, it was found that the proposed method is consistent and zero-stable, hence it is convergent. The proposed method’s efficiency was obtained and a comparison was made in terms of accuracy to some existing methods with similar order or higher than it. This new method is able to solve linear and nonlinear initial value problems of the general second-order ODEs and outperformed existing methods with impressive results. Applications of the new method such as in the Fermi-Pasta-Ulam problem and van der Pol oscillator are discussed.
关键词：Block;Second-order;IVPs;Hermite interpolation;Implicit