An improved Talbot method for numerical Laplace transform inversion

TL;DR

This paper presents an improved Talbot method for faster and more stable numerical inversion of Laplace transforms, especially when the transform is analytic except for the negative real axis.

Contribution

The authors introduce a truncated contour and a stability control mechanism to enhance the classical Talbot method's convergence and robustness.

Findings

Faster convergence with the truncated contour approach.

Enhanced numerical stability through the control mechanism.

Effective performance on transforms from tables and real applications.

Abstract

The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour rather than the classical contour that goes to infinity in the left half-plane, faster convergence is achieved. Second, a control mechanism for improving numerical stability is introduced. These two features are incorporated into a software code, whose performance is assessed on transforms from tables as well as from actual applications. It is shown that even when the transform has singularities off the negative real axis, rapid convergence can still be achieved in many cases.