Approximation of singularly perturbed reaction-diffusion problems by quadratic \(C ^1\)-splines (Q451804)
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scientific article; zbMATH DE number 6085767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of singularly perturbed reaction-diffusion problems by quadratic \(C ^1\)-splines |
scientific article; zbMATH DE number 6085767 |
Statements
Approximation of singularly perturbed reaction-diffusion problems by quadratic \(C ^1\)-splines (English)
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24 September 2012
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A singularly perturbed reaction-diffusion problem is discretised via quadratic \(C^1\)-splines in one dimension. To resolve layers, a modified Shishkin mesh is used. The method is shown to be of almost second order in the maximum norm, uniform in the perturbation parameter. A posteriori error bounds are derived and numerical results are presented.
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reaction-diffusion problems
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spline interpolation
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collocation
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singular perturbations
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a posteriori error estimation
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Shishkin mesh
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numerical results
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0.9221369
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0.9117774
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0.90455234
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