Numerical inversion of laplace transforms using contour methods

Abstract

A numerical method for the inversion of Laplace transforms is presented. The method is based on choosing a suitable contour to replace the usual Bromwich contour. A choice of four contours is considered and an automatic contour setting procedure developed based on piece-wise straight line segments. The choice of contour allows the use of high precision oscillatory integrand methods to be employed, as well as minimizing the resulting errors. The routine is tested on a well-known test set and a comparison made of the various contours. The results are extended to the difficult case of large values of the inversion parameter without any significant increase in computer effort.

Keywords:

• Laplace transforms
• inversion of laplace transforms
• numerical quadrature

C.R. Categories:

• G1.4