Talbot's Method
Despite being widely accepted as a highly accurate method, in the twenty-five years since its
introduction, the Talbot method has received relatively little attention WEIDEMAN1999. Unlike the
Fourier series or Post-Widder approaches, Talbot's method is based on a deformation of the Bromwich
contour. The idea is to replace the contour with one which opens toward the negative real axis
![]() It thus inherently assumes that the physical system damps highly oscillatory terms and is not appropriate for purely conservative problems. From a numerical perspective however, damping the highly oscillatory terms in the inversion integral is a stabilizing procedure since it is these which provide the largest contribution to the error when one performs numerical quadrature of the Laplace inversion integral.
The primary difficulty of the Talbot method is the selection of accurate values for the contour
parameters. The original paper by Talbot is rather lengthly with only a few pages on the derivation
of the contour using the steepest-decent method. The remaining pages are a
detailed discussion of how to determine the parameters from the properties of the function |