Parabolic and hyperbolic contours for computing the Bromwich integral

Weideman, J.; Trefethen, L.

doi:10.1090/S0025-5718-07-01945-X

Parabolic and hyperbolic contours for computing the Bromwich integral
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by J. A. C. Weideman and L. N. Trefethen;

Math. Comp. 76 (2007), 1341-1356

DOI: https://doi.org/10.1090/S0025-5718-07-01945-X

Published electronically: March 7, 2007

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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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