Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods
It is well known that a polynomial-based approximation scheme applied to a singularly perturbed equation is not uniformly convergent over the geometric domain of study. Such scheme results in a numerical solution, say σ which suffers from severe inaccuracies particularly in the boundary layer. What...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000910 |
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| _version_ | 1832550214932627456 |
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| author | Dialla Konate |
| author_facet | Dialla Konate |
| author_sort | Dialla Konate |
| collection | DOAJ |
| description | It is well known that a polynomial-based approximation scheme
applied to a singularly perturbed equation is not uniformly
convergent over the geometric domain of study. Such scheme results
in a numerical solution, say σ which suffers from severe
inaccuracies particularly in the boundary layer. What we say in the
current paper is this: when one uses a grid which is not too
coarse the resulted solution, even being nonuniformly convergent
may be used in an iterated scheme to get a good approximation
solution that is uniformly convergent over the whole geometric
domain of study. |
| format | Article |
| id | doaj-art-5ededc483c38451497bdd569d33ec67f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5ededc483c38451497bdd569d33ec67f2025-02-03T06:07:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124530531310.1155/S0161171200000910Uniformly convergent schemes for singularly perturbed differential equations based on collocation methodsDialla Konate037 Rue de la République, Puteaux 92800, FranceIt is well known that a polynomial-based approximation scheme applied to a singularly perturbed equation is not uniformly convergent over the geometric domain of study. Such scheme results in a numerical solution, say σ which suffers from severe inaccuracies particularly in the boundary layer. What we say in the current paper is this: when one uses a grid which is not too coarse the resulted solution, even being nonuniformly convergent may be used in an iterated scheme to get a good approximation solution that is uniformly convergent over the whole geometric domain of study.http://dx.doi.org/10.1155/S0161171200000910 |
| spellingShingle | Dialla Konate Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods International Journal of Mathematics and Mathematical Sciences |
| title | Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| title_full | Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| title_fullStr | Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| title_full_unstemmed | Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| title_short | Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| title_sort | uniformly convergent schemes for singularly perturbed differential equations based on collocation methods |
| url | http://dx.doi.org/10.1155/S0161171200000910 |
| work_keys_str_mv | AT diallakonate uniformlyconvergentschemesforsingularlyperturbeddifferentialequationsbasedoncollocationmethods |