Abstract
We consider the numerical solution of second kind integral equations of the form
for some given kernelk(t). These equations, usually indicated as of Mellin type, arise in a variety of applications.
In particular, we examine a Nyström interpolant based on the following product quadrature rule:
This rule is obtained by interpolatingu(x) by the Lagrange polynomial associated with the set of Gauss-Radau nodes {x ni}.
Under certain assumptions on the kernelk(t), we are able to prove the stability of our interpolant and derive convergence estimates.
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Work performed under the auspices of the Ministero dell'Università e della Ricerca Scientifica e Tecnologica of Italy.
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Monegato, G. A stable Nyström interpolant for some Mellin convolution equations. Numer Algor 11, 271–283 (1996). https://doi.org/10.1007/BF02142502
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DOI: https://doi.org/10.1007/BF02142502