引入Ostrowski同伦延拓法求解非线性方程

Hafizudin Mohamad Nor, A. I. Asnor, Z. R. Yahya, M. Z. Ahmad
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引用次数: 0

摘要

本文采用经典方法和强大方法相结合的方法求解了一类非线性方程。基本上,众所周知,同伦延拓法(HCM)是一种强大的方法,已被用于解决经典方法的问题。本文提出了一种新的方法,即Ostrowski同伦延拓法(Ostrowski- hcm),以克服经典Ostrowski方法在初始猜想不准确时产生的散度问题。简单地说,当给定函数的导数在起始点等于零时,问题就出现了。因此,除零会使该方案无效。此外,利用数学软件Mathematica 7.0对Ostrowski-HCM结果进行了实现。因此,从结果的分析,证明了Ostrowski-HCM是可靠的,有利于求解非线性方程。
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Introduction of Ostrowski Homotopy Continuation Method for Solving Nonlinear Equations Using Mathematica
The solution to a nonlinear equation is found in this study by combining a classical and a powerful method. Basically, it is well known that the Homotopy Continuation Method (HCM) is a powerful method that has been used for solving the problem of the classical method. A new approach is introduced in this study which is known as the Ostrowski Homotopy Continuation Method (Ostrowski-HCM) with a purpose to overcome the divergence problem that arises from the classical Ostrowski’s method when a bad initial guess is used. To put it simply, when the derivative of a given function at the starting point is equal to zero, the problem arises. As a result, the division by zero renders the scheme invalid. In addition, a mathematical software, Mathematica 7.0, is used to implement the Ostrowski-HCM results. Thus, from the analysis of the results, it is proven that the Ostrowski-HCM is reliable and advantageous for solving the nonlinear equation.
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来源期刊
Songklanakarin Journal of Science and Technology
Songklanakarin Journal of Science and Technology Multidisciplinary-Multidisciplinary
CiteScore
1.10
自引率
0.00%
发文量
0
审稿时长
25 weeks
期刊介绍: Songklanakarin Journal of Science and Technology (SJST) aims to provide an interdisciplinary platform for the dissemination of current knowledge and advances in science and technology. Areas covered include Agricultural and Biological Sciences, Biotechnology and Agro-Industry, Chemistry and Pharmaceutical Sciences, Engineering and Industrial Research, Environmental and Natural Resources, and Physical Sciences and Mathematics. Songklanakarin Journal of Science and Technology publishes original research work, either as full length articles or as short communications, technical articles, and review articles.
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