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Mathematics of Computation

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Parabolic and hyperbolic contours for computing the Bromwich integral

Authors: J. A. C. Weideman and L. N. Trefethen
Journal: Math. Comp. 76 (2007), 1341-1356
MSC (2000): Primary 65D30, 44A10
Published electronically: March 7, 2007
MathSciNet review: 2299777
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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

L. N. Trefethen
Affiliation: Oxford University Computing Laboratory, Wolfson Bldg., Parks Road, Oxford OX1 3QD, United Kingdom
MR Author ID: 174135

Keywords: Laplace transform, Talbot’s method, trapezoidal rule, fractional differential equation
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.