{"title":"求解一阶刚性微分方程的七步块多步方法","authors":"S. Gebregiorgis, H. Muleta","doi":"10.4314/mejs.v12i1.5","DOIUrl":null,"url":null,"abstract":"In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method. \n Keywords: Power series, Collocation, Interpolation, Block method, Stiff.","PeriodicalId":18948,"journal":{"name":"Momona Ethiopian Journal of Science","volume":"12 1","pages":"72-82"},"PeriodicalIF":0.3000,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations\",\"authors\":\"S. Gebregiorgis, H. Muleta\",\"doi\":\"10.4314/mejs.v12i1.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method. \\n Keywords: Power series, Collocation, Interpolation, Block method, Stiff.\",\"PeriodicalId\":18948,\"journal\":{\"name\":\"Momona Ethiopian Journal of Science\",\"volume\":\"12 1\",\"pages\":\"72-82\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Momona Ethiopian Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4314/mejs.v12i1.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Momona Ethiopian Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/mejs.v12i1.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations
In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.
Keywords: Power series, Collocation, Interpolation, Block method, Stiff.
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