Wavelet-Galerkin method for the singular perturbation problem with boundary layers (Q2739078)
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scientific article; zbMATH DE number 1643419
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wavelet-Galerkin method for the singular perturbation problem with boundary layers |
scientific article; zbMATH DE number 1643419 |
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9 June 2002
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numerical examples
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wavelet-Galerkin method
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singular perturbation
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boundary layer
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boundary value problem
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preconditioning
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condition number
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error estimate
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computational complexity
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Wavelet-Galerkin method for the singular perturbation problem with boundary layers (English)
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The author solves numerically the singular perturbation boundary value problem \((-\varepsilon u'+bu)'=f\) on \(\Omega=(0,1)\) with \(u(0)=u(1)=0\). Because of the presence of boundary layers, approximation spaces with different scales and boundary bases are used in the wavelet-Galerkin method. Thus, high accuracy is obtained with a reasonable computational effort. An explicit diagonal preconditioning results in a bounded condition number of the stiff matrix. An error estimate and a computational complexity analysis are presented. Examples illustrate the method.
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