Inversion of the Laplace transform from the real axis using an adaptive iterative method
This work addresses the challenging problem of Laplace transform inversion from real-axis data, which is relevant for applications in engineering and physics, but the method is incremental as it builds on existing quadrature-based approaches.
The paper presents a new adaptive iterative method for inverting the Laplace transform from the real axis, assuming the unknown function is continuous with compact support. The method includes an adaptive stopping rule that ensures convergence of the approximate solution.
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.