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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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