Inversion of the Laplace transform from the real axis using an adaptive iterative method

TL;DR

This paper introduces an adaptive iterative method based on quadrature formulas for inverting the Laplace transform from the real axis, ensuring convergence to the unknown function with known support.

Contribution

The paper presents a novel adaptive iterative approach with a stopping rule for stable inversion of the Laplace transform from the real axis.

Findings

Method guarantees convergence to the true function

Adaptive stopping rule improves stability

Applicable to functions with known compact support

Abstract

In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to $f(t)$, are proposed in this paper.