Comparative study on One-Dimensional Numerical Inverse Laplace Transform Methods for Electrical Engineering

Abstract

In various engineering and science problems we are often confronted with the need to applythe Laplace transform to simplify the problem and get our solution, however in many cases when solvingdifferential equations, systems with lumped parameters or more generally to solve rational, irrationalor transcendental functions, the need to use numerical inverse Laplace transforms arise, mainly due tothe difficult analytic inversions back to the real time domain. In this paper a review of some numericalmethods are listed and compared together with functions that are typically used in engineering andtelecommunications in order to evaluate these different methods based on their performance, accuracy,stability and computational speed, with the motivation to find a relatively suitable and universal 1DNILT method. These results are helpful to decide which of the methods are more likely to be consideredfor further development into higher dimensions, to solve systems with more than one variable.In various engineering and science problems we are often confronted with the need to applythe Laplace transform to simplify the problem and get our solution, however in many cases when solvingdifferential equations, systems with lumped parameters or more generally to solve rational, irrationalor transcendental functions, the need to use numerical inverse Laplace transforms arise, mainly due tothe difficult analytic inversions back to the real time domain. In this paper a review of some numericalmethods are listed and compared together with functions that are typically used in engineering andtelecommunications in order to evaluate these different methods based on their performance, accuracy,stability and computational speed, with the motivation to find a relatively suitable and universal 1DNILT method. These results are helpful to decide which of the methods are more likely to be consideredfor further development into higher dimensions, to solve systems with more than one variable.