{"title":"一阶常微分方程非线性初值问题解的标准后向微分格式","authors":"Odekunle","doi":"10.4314/GJMAS.V3I1.21353","DOIUrl":null,"url":null,"abstract":"This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give better results than Euler backward method and trapezoidal method near a singular point. KEY WORDS: backward differentiation scheme, collocation, initial value problems. Global Jnl Mathematical Sciences Vol.3(1) 2004: 57-63","PeriodicalId":126381,"journal":{"name":"Global Journal of Mathematical Sciences","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR SOLUTION OF NONLINEAR INITIAL VALUE PROBLEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS\",\"authors\":\"Odekunle\",\"doi\":\"10.4314/GJMAS.V3I1.21353\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give better results than Euler backward method and trapezoidal method near a singular point. KEY WORDS: backward differentiation scheme, collocation, initial value problems. Global Jnl Mathematical Sciences Vol.3(1) 2004: 57-63\",\"PeriodicalId\":126381,\"journal\":{\"name\":\"Global Journal of Mathematical Sciences\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Global Journal of Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4314/GJMAS.V3I1.21353\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Global Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/GJMAS.V3I1.21353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR SOLUTION OF NONLINEAR INITIAL VALUE PROBLEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give better results than Euler backward method and trapezoidal method near a singular point. KEY WORDS: backward differentiation scheme, collocation, initial value problems. Global Jnl Mathematical Sciences Vol.3(1) 2004: 57-63