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An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinear...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4942452/ https://www.ncbi.nlm.nih.gov/pubmed/27462514 http://dx.doi.org/10.1186/s40064-016-2753-9 |
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author | Xie, Lie-jun Zhou, Cai-lian Xu, Song |
author_facet | Xie, Lie-jun Zhou, Cai-lian Xu, Song |
author_sort | Xie, Lie-jun |
collection | PubMed |
description | In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. |
format | Online Article Text |
id | pubmed-4942452 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-49424522016-07-26 An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method Xie, Lie-jun Zhou, Cai-lian Xu, Song Springerplus Research In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. Springer International Publishing 2016-07-12 /pmc/articles/PMC4942452/ /pubmed/27462514 http://dx.doi.org/10.1186/s40064-016-2753-9 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Xie, Lie-jun Zhou, Cai-lian Xu, Song An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title | An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title_full | An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title_fullStr | An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title_full_unstemmed | An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title_short | An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
title_sort | effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4942452/ https://www.ncbi.nlm.nih.gov/pubmed/27462514 http://dx.doi.org/10.1186/s40064-016-2753-9 |
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