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On the non-existence of |
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| Authors: | Paul A. Farrell John J. H. Miller Eugene O'Riordan Grigorii I. Shishkin. |
| Affiliation: | Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242 ; Department of Mathematics, Trinity College, Dublin 2, Ireland ; School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland ; Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia |
| Abstract: | In this paper fitted finite difference methods on a uniform mesh with internodal spacing  , are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge  -uniformly in the maximum norm to the solution of the differential equation as the mesh spacing  goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors. |
| Keywords: | Semilinear boundary value problem singular perturbation finite difference scheme $varepsilon$-uniform convergence uniform mesh frozen fitting factor |
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