The noise handling properties of the Talbot algorithm for numerically inverting the Laplace transform. (September 2018)

• Record Type: Journal Article
• Authors: Defreitas, Colin L; Kane, Steve J
• Is Part Of: Journal of algorithms & computational technology. Volume 13(2019)
• Publication Date: 2018-09
• Subjects: Talbot algorithm -- inverse Laplace transform -- Stehfest -- numerical solution to parabolic partial differential equation -- numerical inversion of the Laplace transform; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748301818797069
• Languages: English
• ISSNs: 1748-3018

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, their error handling 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 for "noisy data", the Talbot inversion algorithm performs with greater accuracy when compared to the Fourier series and Stehfest numerical inversion schemes as they are outlined in this paper.