{"title":"Fifth Order Improved Runge-Kutta Nystrom Method Using Trigonometrically-Fitting for Solving Oscillatory Problems","authors":"Waleed J. Hasan, Kasim A. Hussain","doi":"10.22401/anjs.25.4.11","DOIUrl":null,"url":null,"abstract":"In this paper, the Trigonometrically Fitted Improved Runge-KuttaNystrom method is proposed as a novel method with four stages and fifth order for solving oscillatory problems. This method is intended to integrate second-order initial value problems using the trigonometrically fitting approach. To increase the method'saccuracy, the principal frequency of the problem푤∈ℝ, is used. It is discovered that the new method is more precise when compared with the other existing Runge-Kutta Nystrom and IRKN5 methods. To show how well the TFIRKN5 method works, test problems for second-order ordinary differential equations (ODEs) are solved. The numerical outcomes show that the novel approach outperforms methods that have already been published.","PeriodicalId":7494,"journal":{"name":"Al-Nahrain Journal of Science","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Al-Nahrain Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22401/anjs.25.4.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the Trigonometrically Fitted Improved Runge-KuttaNystrom method is proposed as a novel method with four stages and fifth order for solving oscillatory problems. This method is intended to integrate second-order initial value problems using the trigonometrically fitting approach. To increase the method'saccuracy, the principal frequency of the problem푤∈ℝ, is used. It is discovered that the new method is more precise when compared with the other existing Runge-Kutta Nystrom and IRKN5 methods. To show how well the TFIRKN5 method works, test problems for second-order ordinary differential equations (ODEs) are solved. The numerical outcomes show that the novel approach outperforms methods that have already been published.