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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


An error estimate for Stenger's quadrature formula

Authors: S. Beighton and B. Noble
Journal: Math. Comp. 38 (1982), 539-545
MSC: Primary 65D30
MathSciNet review: 645669
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Abstract | References | Similar Articles | Additional Information

Abstract: The basis of this paper is the quadrature formula

$\displaystyle \int_{ - 1}^1 {f(x)\,dx \approx \log q\sum\limits_{m = - M}^M {\f... ...m}}}{{{{(1 + {q^m})}^2}}}f\left( {\frac{{{q^m} - 1}}{{{q^m} + 1}}} \right)} ,} $

where $ q = \exp (2h)$, h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger.

An explicit form of the error is given for the case where the integrand has a factor of the form $ {(1 - x)^\alpha }{(1 + x)^\beta },\alpha ,\beta > - 1$. Application is made to the evaluation of Cauchy principal value integrals with endpoint singularities and an appropriate error form is derived.

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Additional Information

PII: S 0025-5718(1982)0645669-9
Article copyright: © Copyright 1982 American Mathematical Society

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