{"title":"A modified parametric iteration method for solving nonlinear second order BVPs","authors":"A. Ghorbani, M. Gachpazan, Jafar Saberi-Nadjafi","doi":"10.1590/S1807-03022011000300002","DOIUrl":null,"url":null,"abstract":"The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"66 1","pages":"499-515"},"PeriodicalIF":2.5000,"publicationDate":"2011-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational & Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1590/S1807-03022011000300002","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 5
Abstract
The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.
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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