Error Analysis Using Three and Four Stage Eighth Order Embedded Runge-Kutta Method for Sixth Order Ordinary Differential Equation vvi(u)=f(u,v,v',v'',v''',viv)
{"title":"Error Analysis Using Three and Four Stage Eighth Order Embedded Runge-Kutta Method for Sixth Order Ordinary Differential Equation vvi(u)=f(u,v,v',v'',v''',viv)","authors":"Manpreet Kaur, Sangeet Kumar, J. Bhatti","doi":"10.37256/cm.4420232610","DOIUrl":null,"url":null,"abstract":"The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"9 3","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contemporary Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37256/cm.4420232610","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.