Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi
{"title":"Accelerating the Speed of Convergence for High-Order Methods to Solve Equations","authors":"Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi","doi":"10.3390/math12172785","DOIUrl":null,"url":null,"abstract":"This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/math12172785","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.