Digital computation of inverse Laplace transforms

Abstract

This note describes an algorithm for the digital computation of the inverse Laplace transform of a function containing multiple real or complex poles and discusses its advantages and disadvantages.

The algorithm utilizes a well-known, simple mathemat ical technique to evaluate a polynomial and its derivatives at a root of the polynomial. This method allows the nvmerator and denominator polynomials of the function to be treated separately by dividing each repeatedly by a first-order term. Synthetic

division of a first-order term into a polynomial when both contain complex coefficients is particularly suited to digital computation. Execution times for Pottle's algorithm and the algorithm proposed in this paper are compared. The paper concludes with a BASIC program which implements the latter algorithm.