{"title":"一类修正后向微分公式(BDF)型的二阶导数块法求解刚性常微分方程","authors":"Atsi Kaze, Adiku Lydia, Yarima Namuma, G. Kumleng","doi":"10.26634/jmat.11.2.19206","DOIUrl":null,"url":null,"abstract":"In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.","PeriodicalId":297202,"journal":{"name":"i-manager’s Journal on Mathematics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations\",\"authors\":\"Atsi Kaze, Adiku Lydia, Yarima Namuma, G. Kumleng\",\"doi\":\"10.26634/jmat.11.2.19206\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.\",\"PeriodicalId\":297202,\"journal\":{\"name\":\"i-manager’s Journal on Mathematics\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"i-manager’s Journal on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26634/jmat.11.2.19206\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"i-manager’s Journal on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26634/jmat.11.2.19206","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations
In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.
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