{"title":"An Approximation Solution of Linear Differential Equation using Kantorovich Methods","authors":"W. A. Ahmood, Marwa Mohamed Ismaeel","doi":"10.37394/232011.2023.18.2","DOIUrl":null,"url":null,"abstract":"In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Applied and Theoretical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232011.2023.18.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.
期刊介绍：
WSEAS Transactions on Applied and Theoretical Mechanics publishes original research papers relating to computational and experimental mechanics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with fluid-structure interaction, impact and multibody dynamics, nonlinear dynamics, structural dynamics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.
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