An error estimate for Stenger's quadrature formula
S. Beighton and B. Noble
Math. Comp. 38 (1982), 539-545
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Abstract: The basis of this paper is the quadrature formula where , 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 . Application is made to the evaluation of Cauchy principal value integrals with endpoint singularities and an appropriate error form is derived.
Oberhettinger, and F.
G. Tricomi, Tables of integral transforms. Vol. II,
McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in
part, on notes left by Harry Bateman. MR 0065685
Stenger, Integration formulae based on the trapezoidal
formula, J. Inst. Math. Appl. 12 (1973),
103–114. MR 0381261
- A. Erdélyi, Tables of Integral Transforms, Vol. II, McGraw-Hill, New York, 1954. MR 0065685 (16:468c)
- F. Stenger, "Integration formulae based on the trapezoidal formula," J. Inst. Math. Appl., v. 12, 1973, pp. 103-114. MR 0381261 (52:2158)
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