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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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An error estimate for Stenger’s quadrature formula
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by S. Beighton and B. Noble PDF
Math. Comp. 38 (1982), 539-545 Request permission

Abstract:

The basis of this paper is the quadrature formula \[ \int _{ - 1}^1 {f(x) dx \approx \log q\sum \limits _{m = - M}^M {\frac {{2{q^m}}}{{{{(1 + {q^m})}^2}}}f\left ( {\frac {{{q^m} - 1}}{{{q^m} + 1}}} \right )} ,} \] 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
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 539-545
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0645669-9
  • MathSciNet review: 645669