On the numerical Picard iterations with collocations for the initial value problem
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term "numerical" emphasizes that a numerical solution is computed. The method consists in replacing the right hand side of the differential system by Lagrange inte...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2019-09-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | http://localhost/jnaat/journal/article/view/1146 |
| _version_ | 1797786739518996480 |
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| author | Ernest Scheiber |
| author_facet | Ernest Scheiber |
| author_sort | Ernest Scheiber |
| collection | DOAJ |
| description | Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term "numerical" emphasizes that a numerical solution is computed. The method consists in replacing the right hand side of the differential system by Lagrange interpolation polynomials followed by successive approximations. In the case when the number of interpolation point is fixed a convergence result is given. Finally some numerical experiments are reported.
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| first_indexed | 2024-03-13T01:13:07Z |
| format | Article |
| id | doaj.art-dfc46467699a4014996931baf81d6c43 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-03-13T01:13:07Z |
| publishDate | 2019-09-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-dfc46467699a4014996931baf81d6c432023-07-05T17:34:12ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2019-09-01481On the numerical Picard iterations with collocations for the initial value problemErnest Scheiber0retired, RomaniaSome variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term "numerical" emphasizes that a numerical solution is computed. The method consists in replacing the right hand side of the differential system by Lagrange interpolation polynomials followed by successive approximations. In the case when the number of interpolation point is fixed a convergence result is given. Finally some numerical experiments are reported. http://localhost/jnaat/journal/article/view/1146Picard iterationsinitial value problemcollocation |
| spellingShingle | Ernest Scheiber On the numerical Picard iterations with collocations for the initial value problem Journal of Numerical Analysis and Approximation Theory Picard iterations initial value problem collocation |
| title | On the numerical Picard iterations with collocations for the initial value problem |
| title_full | On the numerical Picard iterations with collocations for the initial value problem |
| title_fullStr | On the numerical Picard iterations with collocations for the initial value problem |
| title_full_unstemmed | On the numerical Picard iterations with collocations for the initial value problem |
| title_short | On the numerical Picard iterations with collocations for the initial value problem |
| title_sort | on the numerical picard iterations with collocations for the initial value problem |
| topic | Picard iterations initial value problem collocation |
| url | http://localhost/jnaat/journal/article/view/1146 |
| work_keys_str_mv | AT ernestscheiber onthenumericalpicarditerationswithcollocationsfortheinitialvalueproblem |