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Mathematics of Computation

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Product integration for weakly singular integral equations


Author: Claus Schneider
Journal: Math. Comp. 36 (1981), 207-213
MSC: Primary 65R20; Secondary 45L05
DOI: https://doi.org/10.1090/S0025-5718-1981-0595053-0
MathSciNet review: 595053
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Abstract: The product integration method is used for the numerical solution of weakly singular integral equations of the second kind. These equations often have solutions which have derivative singularities at the endpoints of the range of integration. Therefore, the order of convergence results of de Hoog and Weiss for smooth solutions do not hold in general. In this paper it is shown that their results may be regained for the general case by using an appropriate nonuniform mesh. The spacing of the knot points is defined by the behavior of the solution at the endpoints. If the solution is smooth enough the mesh becomes uniform. Numerical examples are given.


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DOI: https://doi.org/10.1090/S0025-5718-1981-0595053-0
Article copyright: © Copyright 1981 American Mathematical Society