Uniform error estimates of Galerkin methods for monotone Abel-Volterra integral equations on the half-line

Author:
P. P. B. Eggermont

Journal:
Math. Comp. **53** (1989), 157-189

MSC:
Primary 65R20; Secondary 45D05, 47H17

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969485-X

MathSciNet review:
969485

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Abstract: We consider Galerkin methods for monotone Abel-Volterra integral equations of the second kind on the half-line. The theory follows from Kolodner's theory of monotone Hammerstein, equations. We derive the theory from the theory by relating the - and -spectra of operators of the form to one another. Here denotes convolution, and and . As an extra condition we need , with . We also prove the discrete analogue. In particular, we verify that the Galerkin matrix satisfies the "discrete" conditions.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0969485-X

Article copyright:
© Copyright 1989
American Mathematical Society