Wavelet solving process of heat-conduction equation (Q2712461)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wavelet solving process of heat-conduction equation |
scientific article |
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3 January 2002
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heat equation
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differential operator wavelet approximation
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explicit discrete scheme
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Daubechies wavelet
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solutions with singularities
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error estimates
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numerical example
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Wavelet solving process of heat-conduction equation (English)
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This paper discusses the numerical solution of the initial value problem for the one-dimensional linear heat equation. Using the Daubechies wavelet, the authors propose an explicit discrete scheme. The scheme especially adapts to solutions with singularities because of the time-frequency local property of the wavelets. The error estimates of the scheme in \(H^2\)-norm are given. A numerical example is presented. It demonstrates the high accuracy and non-oscillation of the scheme near singularities of the solutions.
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