An Inversion Technique for the Laplace Transform

Abstract

In this paper we use an approximation sequence defined by the Widder Laplace transform inversion formula to provide a practical method for inverting the Laplace transform. The approximation sequence converges uniformly and retains essential structural characteristics of the original function, e.g., nonnegativity, monotonicity, and convexity. Thus, we approximate a distribution function by distribution functions and use enhancement techniques to increase the speed of convergence and to capture the quality of exponential decay. Also, we present a practical computational method illustrated by examples.