Discretization of Volterra integral equations of the first kind

Author:
Hermann Brunner

Journal:
Math. Comp. **31** (1977), 708-716

MSC:
Primary 65R05; Secondary 45L05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0451794-6

MathSciNet review:
0451794

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Abstract: We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregularity of the given integral operator becomes only relevant when selecting a discretization procedure for the moment integrals resulting from collocation. Similar results hold for equations of the second kind.

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0451794-6

Keywords:
First-kind integral equations of Volterra and Abel type,
collocation by piecewise polynomials,
numerical quadrature,
discrete appoximations

Article copyright:
© Copyright 1977
American Mathematical Society