Numerical Inversion of Laplace Transforms Using Laguerre Functions

A method is described for the numerical inversion of Laplace transforms, in which the inverse is obtained as an expansion in terms of orthonormal Laguerre functions. In order for this to be accomplished, the given Laplace transform is expanded in terms of the Laplace transforms of the orthonormal Laguerre functions. The latter expansion is then reduced to a cosine series whose approximate expansion coefficients are obtained by means of trigonometric interpolation. The computational steps have been arranged to facilitate automatic digital computation, and numerical illustrations have been given.