{"title":"常微分方程数值解的倒诺德塞克方法","authors":"V. Bucharskyi","doi":"10.36074/20.11.2020.v5.25","DOIUrl":null,"url":null,"abstract":"where: z = (u, τu, τu, ... , τu ) – Nordsieck’s vector, τ – integration step, М – the number of terms in the Taylor series expansion of the function u(t), D, L – upper triangular and diagonal matrices whose element’s values di,j = { 1 (i−j)! , i ≥ j 0, i < j , li,i = τM−i+1 (M−i+1)! follow from the series expansion, q – a vector of free parameters that determines the properties of the numerical method,","PeriodicalId":235647,"journal":{"name":"MODALITĂȚI CONCEPTUALE DE DEZVOLTARE A ȘTIINȚEI MODERNE- VOLUMEN 5","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"BACKWARD NORDSIECK’S METHODS FOR NUMERICAL SOLVING OF ORDINARY DIFFERENTIAL EQUATIONS\",\"authors\":\"V. Bucharskyi\",\"doi\":\"10.36074/20.11.2020.v5.25\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"where: z = (u, τu, τu, ... , τu ) – Nordsieck’s vector, τ – integration step, М – the number of terms in the Taylor series expansion of the function u(t), D, L – upper triangular and diagonal matrices whose element’s values di,j = { 1 (i−j)! , i ≥ j 0, i < j , li,i = τM−i+1 (M−i+1)! follow from the series expansion, q – a vector of free parameters that determines the properties of the numerical method,\",\"PeriodicalId\":235647,\"journal\":{\"name\":\"MODALITĂȚI CONCEPTUALE DE DEZVOLTARE A ȘTIINȚEI MODERNE- VOLUMEN 5\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"MODALITĂȚI CONCEPTUALE DE DEZVOLTARE A ȘTIINȚEI MODERNE- VOLUMEN 5\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36074/20.11.2020.v5.25\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"MODALITĂȚI CONCEPTUALE DE DEZVOLTARE A ȘTIINȚEI MODERNE- VOLUMEN 5","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36074/20.11.2020.v5.25","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
BACKWARD NORDSIECK’S METHODS FOR NUMERICAL SOLVING OF ORDINARY DIFFERENTIAL EQUATIONS
where: z = (u, τu, τu, ... , τu ) – Nordsieck’s vector, τ – integration step, М – the number of terms in the Taylor series expansion of the function u(t), D, L – upper triangular and diagonal matrices whose element’s values di,j = { 1 (i−j)! , i ≥ j 0, i < j , li,i = τM−i+1 (M−i+1)! follow from the series expansion, q – a vector of free parameters that determines the properties of the numerical method,
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