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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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Parabolic and hyperbolic contours for computing the Bromwich integral
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by J. A. C. Weideman and L. N. Trefethen PDF
Math. Comp. 76 (2007), 1341-1356 Request permission

Abstract:

Some of the most effective methods for the numerical inversion of the Laplace transform are based on the approximation of the Bromwich contour integral. The accuracy of these methods often hinges on a good choice of contour, and several such contours have been proposed in the literature. Here we analyze two recently proposed contours, namely a parabola and a hyperbola. Using a representative model problem, we determine estimates for the optimal parameters that define these contours. An application to a fractional diffusion equation is presented.
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Additional Information
  • J. A. C. Weideman
  • Affiliation: Department of Applied Mathematics, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa
  • Email: weideman@dip.sun.ac.za
  • L. N. Trefethen
  • Affiliation: Oxford University Computing Laboratory, Wolfson Bldg., Parks Road, Oxford OX1 3QD, United Kingdom
  • MR Author ID: 174135
  • Email: LNT@comlab.ox.ac.uk
  • Received by editor(s): December 9, 2005
  • Published electronically: March 7, 2007
  • Additional Notes: The first author was supported by the National Research Foundation in South Africa under grant FA2005032300018
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1341-1356
  • MSC (2000): Primary 65D30, 44A10
  • DOI: https://doi.org/10.1090/S0025-5718-07-01945-X
  • MathSciNet review: 2299777