We describe a FORTRAN implementation, and some related problems, of Talbot's method which numerically solves the inversion problem of almost arbitrary Laplace transforms by means of special contour integration.The basic idea is to take into account computer precision to derive a special contour where integration will be carried out.

No abstract

Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demostrate how this expression can be used in the development of an automatic routine, one in which the user needs to specify only the required accuracy.

A software package based on a modification of the Weeks' method is presented for calculating function values f ( t ) of the inverse Laplace transform. This method requires transform values F ( z ) at arbitrary points in the complex plane, and is suitable when f ( t ) has continuous derivatives of all orders; it is especially attractive when f ( t ) is required at a number of different abscissas t .