Properties of constants for a quadrature formula to evaluate Bromwich’s integral.

Abstract

Further analytical and empirical properties of the weights and abscissae of a quadrature formula for evaluating Bromwich's integral are described. These are then used to determine the parameters which ensure that a set of abscissae (complex in general) all have positive real parts and to estimate, for Laplace transforms that invert exactly, the maximum number of significant figures of accuracy lost due to cancellation when the quadrature formula is computed