Laplace transform inversions using optimal contours in the complex plane

Abstract

A numerical method for computing inverse Laplace transforms is proposed. In this method, the complex contour integral defining the inverse transform is computed over an equivalent contour as proposed by Talbot and Evans. Special contours, called optimal contours, are constructed so that the transformed real integrand decreases exponentially to zero as z runs along such a contour to infinity. The efficient Clenshaw-Curtis quadrature is employed for the final evaluation. The presented method is competitive and compares favourably with those of Talbot and Evans.

Keywords:

• Inverse Laplace transforms
• optimal contours
• clenshaw-curtis quadrature

C.R. Category:

• G 1.4

^∗Present address: Dept. of Computing Nottingham Trent University, Burton St., Nottingham NGI 4BU.

^∗Present address: Dept. of Computing Nottingham Trent University, Burton St., Nottingham NGI 4BU.

Notes

^∗Present address: Dept. of Computing Nottingham Trent University, Burton St., Nottingham NGI 4BU.