Scaling and asymptotic compensation techniques for early-time response calculation by transform methods

Various approaches to improving the computational efficiency in obtaining the early-time response, by inverse Laplace transform, in pulse propagation and transient scattering analysis are described. Depending on the asymptotic characteristics of the response function in the frequency domain, expanding the time scale and shifting the origin of time often result in accelerated convergence of the numerical Bromwich integral. The use of multiplicative functions such as sech (as) to control the asymptotic growth of the response function in the frequency domain enables the early-time return signals in scattering problems to be represented in terms of the superposition of exponential functions.<>