The Mathematical Institute, University of Oxford, Eprints Archive

A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions

Javed, Mohsin and Trefethen, Lloyd N. (2013) A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions. Technical Report. Proceedings of the Royal Society A. (Submitted)

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Abstract

The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler–Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic functions in another.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1749
Deposited By: Lotti Ekert
Deposited On:10 Sep 2013 09:37
Last Modified:29 May 2015 19:26

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