On one polynomial method of solving integral equations of the third kind (Q498505)
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scientific article; zbMATH DE number 6486218
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On one polynomial method of solving integral equations of the third kind |
scientific article; zbMATH DE number 6486218 |
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On one polynomial method of solving integral equations of the third kind (English)
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28 September 2015
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Fredholm linear integral equations of the third kind on \([0,1]\) are approached in the space of distributions for obtaining the approximate solution. A special variant of the subdomain-collocation method is proposed by using the Chebyshev nodes of the first kind and a basis of Hermite polynomials. In the hypothesis of unique solvability for the integral equation of the third kind, the convergence of the proposed method is proved by providing the error estimate. The method is illustrated by an example showing the form of the error estimate. Finally, the stability of the method is pointed out.
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Fredholm integral equation of the third kind
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space of distributions
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approximate solution
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subdomain-collocation method
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numerical example
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error estimate
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convergence
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stability
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0.90606290102005
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0.8846035599708557
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