A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform

In recent years many results have been obtained in the field of the numerical inversion of Laplace transforms. Among them, a very accurate and general method is due to Talbot: this method approximates the value of the inverse Laplace transform f(t) , for t fixed, using the complex values of the Laplace transform F(s) sampled on a suitable contour of the complex plane. On the basis of the interest raised by Talbot's method implementation, the author has been induced to investigate more deeply the possibilities of this method and has been able to generalize Talbot's method, to approximate simultaneously several values of f(t) using the same sampling values of the Laplace transform. In this way, the only unfavorable aspect of the classical Talbot method, that is, that of recomputing all of the samples of F(s) for each t , has been eliminated.