An accurate numerical inversionof Laplace transforms based on the location of their poles

We introduce an efficient and easily implemented numerical method for the inversion of Laplace transforms, using the analytic continuation of integrands of Bromwichʹs integrals. After deforming the Bromwichʹs contours so that it consists of the union of small circles around singular points, we evaluate the Bromwichʹs integrals by quadrature rules. We prove that the error bound of our method has spectral accuracy of type N + eps/ P, 0 < < 1 and provide several numerical examples.