{"title":"A new efficient two-step iterative method for solving absolute value equations","authors":"Alamgir Khan, Javed Iqbal, Rasool Shah","doi":"10.1108/ec-11-2023-0781","DOIUrl":null,"url":null,"abstract":"<h3>Purpose</h3>\n<p>This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method.</p><!--/ Abstract__block -->\n<h3>Design/methodology/approach</h3>\n<p>We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method.</p><!--/ Abstract__block -->\n<h3>Findings</h3>\n<p>The paper provides empirical insights into how to solve a system of absolute value equations.</p><!--/ Abstract__block -->\n<h3>Originality/value</h3>\n<p>This paper fulfills an identified need to study absolute value equations.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":"18 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Computations","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1108/ec-11-2023-0781","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Purpose
This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method.
Design/methodology/approach
We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method.
Findings
The paper provides empirical insights into how to solve a system of absolute value equations.
Originality/value
This paper fulfills an identified need to study absolute value equations.
期刊介绍:
The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice.
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