Compressible fluid flow and the approximation of iterated integrals of a singular function

Abstract

A computer implementation of Bergman’s solution to the initial value problem for the partial differential equation of compressible fluid flow is described. This work necessitated the discovery of an efficient approximation to the iterated indefinite integrals of an implicitly defined real function of a real variable with a singularity which is not included in the possible domains of integration. The method of approximation used here and the subsequently derived error bounds appear to have rather general applications for the approximation of the iterated integrals of a singular function of one real variable.