Optimized numerical inverse Laplace transformation

TL;DR

This paper introduces an optimized numerical inverse Laplace transformation method that enhances accuracy by incorporating the transform function and time point, surpassing existing AWF-based methods.

Contribution

It presents a novel NILT procedure that improves accuracy by utilizing additional information, unlike traditional AWF methods that are independent of these factors.

Findings

Enhanced accuracy in inverse Laplace transforms

Method outperforms traditional AWF approaches

Applicable to various transform functions and time points

Abstract

Among the numerical inverse Laplace transformation (NILT) methods, those that belong to the Abate-Whitt framework (AWF) are considered to be the most efficient ones currently. It is a characteristic feature of the AWF NILT procedures that they are independent of the transform function and the time point of interest. In this work we propose an NILT procedure that goes beyond this limitation and optimize the accuracy of the NILT utilizing also the transform function and the time point of interest.