Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations
In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and a...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/1803107 |
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| author | Ahmed Farooq Qasim Ekhlass S. AL-Rawi |
| author_facet | Ahmed Farooq Qasim Ekhlass S. AL-Rawi |
| author_sort | Ahmed Farooq Qasim |
| collection | DOAJ |
| description | In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in comparison with other traditional techniques and the arrangements methodology is extremely straightforward and few emphasis prompts high exact solution. The numerical outcomes showed that the acquired estimated solutions were in appropriate concurrence with the correct solution. |
| format | Article |
| id | doaj-art-e5c935da68ce40398021c964ee08cee9 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e5c935da68ce40398021c964ee08cee92025-08-20T02:21:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/18031071803107Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential EquationsAhmed Farooq Qasim0Ekhlass S. AL-Rawi1College of Computer Sciences and Mathematics, University of Mosul, IraqCollege of Computer Sciences and Mathematics, University of Mosul, IraqIn this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in comparison with other traditional techniques and the arrangements methodology is extremely straightforward and few emphasis prompts high exact solution. The numerical outcomes showed that the acquired estimated solutions were in appropriate concurrence with the correct solution.http://dx.doi.org/10.1155/2018/1803107 |
| spellingShingle | Ahmed Farooq Qasim Ekhlass S. AL-Rawi Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations Journal of Applied Mathematics |
| title | Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations |
| title_full | Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations |
| title_fullStr | Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations |
| title_full_unstemmed | Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations |
| title_short | Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations |
| title_sort | adomian decomposition method with modified bernstein polynomials for solving ordinary and partial differential equations |
| url | http://dx.doi.org/10.1155/2018/1803107 |
| work_keys_str_mv | AT ahmedfarooqqasim adomiandecompositionmethodwithmodifiedbernsteinpolynomialsforsolvingordinaryandpartialdifferentialequations AT ekhlasssalrawi adomiandecompositionmethodwithmodifiedbernsteinpolynomialsforsolvingordinaryandpartialdifferentialequations |