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Error expansions for multidimensional trapezoidal rules with Sidi transformations

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Abstract

In 1993, Sidi introduced a set of trigonometric transformations x = ψ(t) that improve the effectiveness of the one-dimensional trapezoidal quadrature rule for a finite interval. In this paper, we extend Sidi's approach to product multidimensional quadrature over [0,1]N. We establish the Euler–Maclaurin expansion for this rule, both in the case of a regular integrand function f(x) and in the cases when f(x) has homogeneous singularities confined to vertices.

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Authors and Affiliations

  1. Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium

    P. Verlinden

  2. The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, IL, 60637, USA

    D.M. Potts

  3. Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL, 60439, USA

    J.N. Lyness

Authors
  1. P. Verlinden
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  2. D.M. Potts
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  3. J.N. Lyness
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Verlinden, P., Potts, D. & Lyness, J. Error expansions for multidimensional trapezoidal rules with Sidi transformations. Numerical Algorithms 16, 321–347 (1997). https://doi.org/10.1023/A:1019155601289

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