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Mathematics of Computation

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Convergence of product integration rules over $ (0,\infty)$ for functions with weak singularities at the origin

Authors: G. Mastroianni and G. Monegato
Journal: Math. Comp. 64 (1995), 237-249
MSC: Primary 65D30
MathSciNet review: 1265016
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Abstract: In this paper we consider integrals of the form

$\displaystyle \int_0^\infty {{e^{ - x}}K(x,y)f(x)dx,} $

with $ f \in {C^p}[0,\infty ) \cap {C^q}(0,\infty ),q \geq p \geq 0$, and $ {x^i}{f^{(p + i)}}(x) \in C[0,\infty ),i = 1, \ldots ,q - p$, when $ q > p$. They appear for instance in certain Wiener-Hopf integral equations and are of interest if one wants to solve these by a Nyström method.

To discretize the integral above, we propose to use a product rule of interpolatory type based on the zeros of Laguerre polynomials. For this rule we derive (weighted) uniform convergence estimates and present some numerical examples.

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Article copyright: © Copyright 1995 American Mathematical Society

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