The Accurate Numerical Inversion of Laplace Transforms

Abstract

Numerical inversion of almost arbitrary Laplace transforms, for any value of t, to any prescribed accuracy up to atleast three-quarters of the computer precision, is effected by trapezoidal integration along a special contour. The required number of points depends on t, the accuracy, and the transform singularity positions, and for moderate t is typically 11 for errors of order 10⁻⁶, 18 for order 10⁻¹⁰, 35 for order 10⁻²⁰(with double precision working).