The Salzer Summation and the numerical inversion of the Laplace Transform: performance analysis for oscillatory, exponential and logarithmic functions

This article presents a study of the Salzer Summation, a technique for the numerical inversion of the Laplace Transform, applied to the inversion of five elementary functions with different behaviors: two oscillatory, two exponential and one logarithmic. Three of the functions studied have a variable parameter a (factor incorporated to investigate the efficiency of the method in dealing with functions of the same class). The algorithm's performance was analyzed for each value of M (number of terms in the sum) and parameter a chosen, through the Mean Absolute Error, graphical representation and execution times approximate. For the set of five functions presented (and for each a), the optimal value of M was determined. It was found that a does not significantly influence the execution time, unlike the parameter M, which directly interferes. Also, it was concluded that for oscillatory functions, the method presents convergence difficulties as the frequency increases