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Recent Developments in the Solution of Nonlinear Differential Equations最新文献

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Multiple Solutions for Some Classes Integro-Dynamic Equations on Time Scales 时间尺度上一类积分动力方程的多重解
Recent Developments in the Solution of Nonlinear Differential Equations Pub Date : 2021-09-08 DOI: 10.5772/intechopen.95621
Svetlin G. Georgiev
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引用次数: 0
Continuous One Step Linear Multi-Step Hybrid Block Method for the Solution of First Order Linear and Nonlinear Initial Value Problem of Ordinary Differential Equations 常微分方程一阶线性和非线性初值问题的连续一步线性多步混合块解法
Recent Developments in the Solution of Nonlinear Differential Equations Pub Date : 2021-09-08 DOI: 10.5772/intechopen.95619
Kamoh Nathaniel, K. Geoffrey, S. Joshua
{"title":"Continuous One Step Linear Multi-Step Hybrid Block Method for the Solution of First Order Linear and Nonlinear Initial Value Problem of Ordinary Differential Equations","authors":"Kamoh Nathaniel, K. Geoffrey, S. Joshua","doi":"10.5772/intechopen.95619","DOIUrl":"https://doi.org/10.5772/intechopen.95619","url":null,"abstract":"In this paper, a collocation approach for solving initial value problem of ordinary differential equations (ODEs) of the first order is presented. This approach consists of reducing the problem to a set of linear multi-step algebraic equations by approximating the ODE with a shifted Legendre polynomial basis function to determine the unknown constants. The proposed method is simple and efficient; it approximates the solutions very closely to the closed form solutions. Some problems were considered using Maple Software to illustrate the simplicity, efficiency and accuracy of the method. The results obtained revealed that the hybrid method can be suitable candidate for all forms of first order initial value problems of ordinary differential equations.","PeriodicalId":368291,"journal":{"name":"Recent Developments in the Solution of Nonlinear Differential Equations","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124327516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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