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 nonperiodicity 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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