Title: The Noise Handling Properties of the Talbot Algorithm for Numerically Inverting the Laplace Transform,
Abstract: This paper examines the noise handling properties of three of the most widely
used algorithms for numerically inverting the Laplace Transform. After
examining the genesis of the algorithms, the regularization properties are
evaluated through a series of standard test functions in which noise is added
to the inverse transform. Comparisons are then made with the exact data. Our
main finding is that the Talbot inversion algorithm is very good at handling
noisy data and performs much better than the Fourier Series and Stehfest
numerical inversion schemes as outlined in this paper. This offers a
considerable advantage for it's use in inverting the Laplace Transform when
seeking numerical solutions to time dependent differential equations.