A numerical method for locating the abscissa of convergence of a laplace transform function with no singularity at infinity

Abstract

The knowledge of the abscissa of convergence σ₀ of a Laplace Transform function F(s), is of primary interest in the field of the numerical inversion of the Laplace Transform itself.

In this paper we propose a method for locating σ₀ when F(s) has no singularity at infinity. The method actually finds an approximation of the real part of the rightmost singularity of F(s).

The method is essentially based on a particular Moebius transformation which maps the extended complex plane into itself; this transformation allows us to build a sequence of values which converges to σ₀.

Keywords:

• Laplace transform inversion
• abscissa of convergence
• Moebius transformation

C.R. Classification:

• G.1.2
• G.1.9