Optimizing Talbot's Contours for the Inversion of the Laplace Transform

Report

Talbot's method for the numerical inversion of the Laplace Transform consists of numerically integrating the Bromwich integral on a special contour by means of the trapezoidal or midpoint rules. In this paper we address the issue of how to choose the parameters that define the contour, for the particular situation when parabolic PDEs are solved. In the process the well known subgeometric convergence rate O(e -c \sqrt N) of this method is improved to the geometric rate O(e -cN) with N the number of nodes in the integration rule. The value of the maximum decay rate c is explicitly determined. Numerical results involving two versions of the heat equation are presented. With the choice of parameters derived here, the rule-of-thumb is that to achieve an accuracy of 10 -l at any given time t, the associated elliptic problem has to be solved no more that l times. Supported by the National Research Foundation in South Africa under grant NRF5289

Authors: Weideman, J

• Publisher: Unspecified
• Publication date: 2005-03-01