On the numerical inversion of the Laplace transform of certain holomorphic mappings

The paper considers the numerical inversion by means of a quadrature formula based on the sinc function, of the Laplace transform of an original mapping which is analytic in some sector containing the half axis x≥0. It is shown that the classical estimate O(e-c√n) improves to O(e-cn/lnn, where n stands for the number of nodes used in the quadrature. The method is illustrated in the context of an evolutionary equation with memory.