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

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