A note on the convergence of product integration and Galerkin method for weakly singular integral equations (Q1372713)
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scientific article; zbMATH DE number 1088840
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the convergence of product integration and Galerkin method for weakly singular integral equations |
scientific article; zbMATH DE number 1088840 |
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A note on the convergence of product integration and Galerkin method for weakly singular integral equations (English)
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14 December 1997
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The paper deals with weakly singular Fredholm type integral equations, where the kernels and their derivatives satisfy algebraic conditions studied by \textit{G. Vainikko} and \textit{A. Pedas} [J. Aust. Math. Soc., Ser. B. 22, 419-430 (1981; Zbl 0475.65085)]. The author obtains the optimal convergence of product integration and Galerkin methods using piecewise polynomials on suitably graded meshes. For proper quadrature rules and iterated Galerkin solutions superconvergence results are obtained.
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weak singularities
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graded mesh
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weakly singular Fredholm type integral equations
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convergence
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product integration and Galerkin methods
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superconvergence
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