Algebraic inversion of the Laplace transform

A new algebraic scheme for inverting Laplace transforms of smooth functions is presented. Expansion of the Laplace transform F(s) in descending powers of s is used to construct the Taylor series of the corresponding time function f(t). This is done through entirely algebraic evaluations of F(s) at symmetric points around circles in the complex plane. Test functions are used to examine the method and the results show good convergence over a broad region near t = 0. The method is especially well-suited to computer-based inversion of Laplace transform.