Algorithm 981: Talbot Suite DE: Application of Modified Talbot’s Method to Solve Differential Problems

In order to solve a differential problem, the Laplace Transform method, when applicable, replaces the problem with a simpler one; the solution is obtained by solving the new problem and then by computing the inverse Laplace Transform of this function. In a numerical context, since the solution of the transformed problem consists of a sequence of Laplace Transform samples, most of the software for the numerical inversion cannot be used since the transform, among parameters, must be passed as a function. To fill this gap, we present Talbot Suite DE, a C software collection for Laplace Transform inversions, specifically designed for these problems and based on Talbot’s method. It contains both sequential and parallel implementations; the latter is accomplished by means of OpenMP.We also report some performance results. Aimed at non-expert users, the software is equipped with several examples and a User Guide that includes the external documentation, explains how to use all the sample code, and reports its results about accuracy and efficiency. Some examples are entirely in C and others combine different programming languages (C/MATLAB, C/FORTRAN). The User Guide also contains useful hints to avoid possible errors issued during the compilation or execution of mixed-language code.