{"title":"On the Contraharmonic-mean Newton’s method(CHN)","authors":"I. Argyros, Manoj K. Singh","doi":"10.47974/jim-1448","DOIUrl":null,"url":null,"abstract":"The objective of this study is to investigate the Contraharmonic-mean Newton’s method (CHN) for solving equations in Banach space. Local analysis has been performed by Taylor’s expansion utilizing high order derivatives and also using only the first derivatives appearing on the method. We have checked the theoretical results by comparing the CHN method with the Newton’s and related third order methods by Weerakoon et al. utilizing some test functions. The theoretical and numerical results are examined by the dynamical analysis of a selected test function.","PeriodicalId":46278,"journal":{"name":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF INTERDISCIPLINARY MATHEMATICS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47974/jim-1448","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The objective of this study is to investigate the Contraharmonic-mean Newton’s method (CHN) for solving equations in Banach space. Local analysis has been performed by Taylor’s expansion utilizing high order derivatives and also using only the first derivatives appearing on the method. We have checked the theoretical results by comparing the CHN method with the Newton’s and related third order methods by Weerakoon et al. utilizing some test functions. The theoretical and numerical results are examined by the dynamical analysis of a selected test function.
期刊介绍：
The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.
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