Parameter N Influence on the Fixed-Talbot Algorithm for the Laplace Transform Numerical Inversion

Abstract

In this paper, Fixed-Talbot method computational aspects are explored for Laplace Transform numerical inversion and its efficiency in the treatment of a set of elementary functions of an exponential, oscillatory and logarithmic nature, based on the influence investigation of free parameter N. The numerical results are compared to the analytical solution while calculating the absolute error. The best value for N was determined in each studied function class, where the method presents satisfactory results. It was observed that increasing the number of terms in the summation for approximation (beyond the optimal value) doesn’t imply obtaining more refined results. In general, based on the data obtained, it was concluded that Fixed-Talbot method is efficient for the inversion of all classes of elementary functions evaluated in this article.

Keywords

• Laplace Transform
• Inverse Transform
• Numerical Methods
• Fixed-Talbot