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 |
| Published: |
Hindawi Limited
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000910 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |