{"title":"用八阶和九阶RUNGE-KUTTA型方法求解常微分方程vvi（u）=f（u，v，v'，v''，v''）","authors":"Manpreet Kaur, Sangeet Kumar, J. Bhatti","doi":"10.22452/mjs.vol42no2.5","DOIUrl":null,"url":null,"abstract":"The present paper presents the numerical conclusion to solve sixth order initial value ordinary differential equation (ODE). The concept of order conditions for three stage eighth order (RKSD8) & four stage ninth order Runge-Kutta methods (RKSD9) has been derived for finding global truncation error of differential equation The global and local truncated errors norms, zero stability of extended Runge-Kutta method (RK) is well defined and demonstrated with the help of an example.","PeriodicalId":18094,"journal":{"name":"Malaysian journal of science","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SOLUTION OF ORDINARY DIFFERENTIAL EQUATION vvi (u)=f(u,v,v',v'',v''') USING EIGHTH AND NINTH ORDER RUNGE-KUTTA TYPE METHOD\",\"authors\":\"Manpreet Kaur, Sangeet Kumar, J. Bhatti\",\"doi\":\"10.22452/mjs.vol42no2.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present paper presents the numerical conclusion to solve sixth order initial value ordinary differential equation (ODE). The concept of order conditions for three stage eighth order (RKSD8) & four stage ninth order Runge-Kutta methods (RKSD9) has been derived for finding global truncation error of differential equation The global and local truncated errors norms, zero stability of extended Runge-Kutta method (RK) is well defined and demonstrated with the help of an example.\",\"PeriodicalId\":18094,\"journal\":{\"name\":\"Malaysian journal of science\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Malaysian journal of science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22452/mjs.vol42no2.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Malaysian journal of science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22452/mjs.vol42no2.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
SOLUTION OF ORDINARY DIFFERENTIAL EQUATION vvi (u)=f(u,v,v',v'',v''') USING EIGHTH AND NINTH ORDER RUNGE-KUTTA TYPE METHOD
The present paper presents the numerical conclusion to solve sixth order initial value ordinary differential equation (ODE). The concept of order conditions for three stage eighth order (RKSD8) & four stage ninth order Runge-Kutta methods (RKSD9) has been derived for finding global truncation error of differential equation The global and local truncated errors norms, zero stability of extended Runge-Kutta method (RK) is well defined and demonstrated with the help of an example.
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