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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Uniform error estimates of Galerkin methods for monotone Abel-Volterra integral equations on the half-line
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by P. P. B. Eggermont PDF
Math. Comp. 53 (1989), 157-189 Request permission


We consider Galerkin methods for monotone Abel-Volterra integral equations of the second kind on the half-line. The ${L^2}$ theory follows from Kolodner’s theory of monotone Hammerstein, equations. We derive the ${L^\infty }$ theory from the ${L^2}$ theory by relating the ${L^2}$- and ${L^\infty }$-spectra of operators of the form $x \to b \ast (ax)$ to one another. Here $\ast$ denotes convolution, and $b \in {L^1}$ and $a \in {L^\infty }$. As an extra condition we need $b(t) = O({t^{ - \alpha - 1}})$, with $\alpha > 0$. We also prove the discrete analogue. In particular, we verify that the Galerkin matrix satisfies the "discrete" conditions.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 157-189
  • MSC: Primary 65R20; Secondary 45D05, 47H17
  • DOI:
  • MathSciNet review: 969485