{"title":"Super implicit two-step collocation methods for ordinary differential equations","authors":"L. Taheri Koltape, G. Hojjati, S. Fazeli, A. Abdi","doi":"10.1007/s40314-024-02848-7","DOIUrl":null,"url":null,"abstract":"<p>This paper introduces a class of two-step collocation methods for the numerical solution of ordinary differential equations. These methods which are equipped with the future point technique and described in two types, to approximate the solution in each step, use the numerical solution in some points in the two previous subintervals as well as in the future subinterval. The superior features of the proposed methods in convergence order and stability in comparison with the similar methods are analyzed. The achieved improvements are verified by giving some numerical experiments.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"43 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40314-024-02848-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces a class of two-step collocation methods for the numerical solution of ordinary differential equations. These methods which are equipped with the future point technique and described in two types, to approximate the solution in each step, use the numerical solution in some points in the two previous subintervals as well as in the future subinterval. The superior features of the proposed methods in convergence order and stability in comparison with the similar methods are analyzed. The achieved improvements are verified by giving some numerical experiments.
期刊介绍：
Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics).
The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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