Premium
Multi‐precision Laplace transform inversion
Author(s) -
Abate J.,
Valkó P. P.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.995
Subject(s) - laplace transform , inversion (geology) , post's inversion formula , two sided laplace transform , algorithm , inverse laplace transform , mellin transform , laplace transform applied to differential equations , wynn , mathematics , computer science , mathematical analysis , geology , fractional fourier transform , fourier transform , paleontology , fourier analysis , structural basin , green's function for the three variable laplace equation , linguistics , philosophy
For the numerical inversion of Laplace transforms we suggest to use multi‐precision computing with the level of precision determined by the algorithm. We present two such procedures. The Gaver–Wynn–Rho (GWR) algorithm is based on a special sequence acceleration of the Gaver functionals and requires the evaluation of the transform only on the real line. The fixed Talbot (FT) method is based on the deformation of the contour of the Bromwich inversion integral and requires complex arithmetic. Both GWR and FT have only one free parameter: M , which is the number of terms in the summation. Both algorithms provide increasing accuracy as M increases and can be realized in a few lines using current Computer Algebra Systems. Copyright © 2004 John Wiley & Sons, Ltd.