{"title":"A new amplification-fitting approach in Newton-Cotes rules to tackling the high-frequency IVPs","authors":"Hosein Saadat , Sanaz Hami Hassan Kiyadeh , Ali Safaie , Ramin Goudarzi Karim , Fayyaz Khodadosti","doi":"10.1016/j.apnum.2024.08.024","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we will further strengthen the fitting technique of the well-known Newton-Cotes rules. First, we fit Boole's rule using the found amplification factor, and then we use it to numerically solve first-order differential equations with oscillating solutions. If the Hamiltonian energy of the system remains almost constant then we investigate whether the new amplification-fitted methods can be used as symplectic methods for numerical integration.</p><p>The obtained results show the high accuracy of the new amplification-fitting Boole's rule-based methods.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"207 ","pages":"Pages 86-96"},"PeriodicalIF":2.2000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424002289","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we will further strengthen the fitting technique of the well-known Newton-Cotes rules. First, we fit Boole's rule using the found amplification factor, and then we use it to numerically solve first-order differential equations with oscillating solutions. If the Hamiltonian energy of the system remains almost constant then we investigate whether the new amplification-fitted methods can be used as symplectic methods for numerical integration.
The obtained results show the high accuracy of the new amplification-fitting Boole's rule-based methods.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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