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Numerical inversion of Laplace transforms using integration and convergence acceleration

Technical Report:

Abstract

This report describes a computational scheme for the numerical inversion of Laplace transforms in the case when all singularities occur on the real line. The determination of the value of the inverse function at a given point t proceeds in four major steps: * Using the Bromwich inversion formula the inverse is represented as an integral over an infinite interval. * By means of the trapezoidal rule this integral is written as an infinite sum. * The sum is converted to a power series. * This power series is evaluated using convergence acceleration. In order to carry out the last step in an efficient way an aggregation of terms is employed to ensure stability and rapid convergence. The truncation error decreases exponentially with the number of terms used and this fact may be exploited in error estimation and the selection of corresponding parameters in the computer programs. If certain general conditions are satisfied, then only a finite number of parameters is required to specify a function with a preselected accuracy. Thus the values of the inverse transform are calculated on a finite grid, and the transform is determined at all other points with interpolation. It is described how to construct  More>>
Authors:
Gustafson, S Aa [1] 
  1. Rogaland Univ., Stavanger (Norway)
Publication Date:
May 01, 1991
Product Type:
Technical Report
Report Number:
SKB-TR-91-18
Reference Number:
SCA: 990200; 052002; PA: AIX-23:012774; SN: 92000638670
Resource Relation:
Other Information: PBD: May 1991
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES; LAPLACE TRANSFORMATION; CONVERGENCE; EXPERIMENTAL DATA; MATHEMATICS; P CODES; RADIOACTIVE WASTE DISPOSAL; RADIONUCLIDE MIGRATION; UNDERGROUND DISPOSAL; 990200; 052002; MATHEMATICS AND COMPUTERS; WASTE DISPOSAL AND STORAGE
OSTI ID:
10111492
Research Organizations:
Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden)
Country of Origin:
Sweden
Language:
English
Other Identifying Numbers:
Other: ON: DE92614105; TRN: SE9100244012774
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
SWDN
Size:
70 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Gustafson, S Aa. Numerical inversion of Laplace transforms using integration and convergence acceleration. Sweden: N. p., 1991. Web.
Gustafson, S Aa. Numerical inversion of Laplace transforms using integration and convergence acceleration. Sweden.
Gustafson, S Aa. 1991. "Numerical inversion of Laplace transforms using integration and convergence acceleration." Sweden.
@misc{etde_10111492,
title = {Numerical inversion of Laplace transforms using integration and convergence acceleration}
author = {Gustafson, S Aa}
abstractNote = {This report describes a computational scheme for the numerical inversion of Laplace transforms in the case when all singularities occur on the real line. The determination of the value of the inverse function at a given point t proceeds in four major steps: * Using the Bromwich inversion formula the inverse is represented as an integral over an infinite interval. * By means of the trapezoidal rule this integral is written as an infinite sum. * The sum is converted to a power series. * This power series is evaluated using convergence acceleration. In order to carry out the last step in an efficient way an aggregation of terms is employed to ensure stability and rapid convergence. The truncation error decreases exponentially with the number of terms used and this fact may be exploited in error estimation and the selection of corresponding parameters in the computer programs. If certain general conditions are satisfied, then only a finite number of parameters is required to specify a function with a preselected accuracy. Thus the values of the inverse transform are calculated on a finite grid, and the transform is determined at all other points with interpolation. It is described how to construct the grid to guarantee that the resulting error does not surpass a bound, defined by the user. An inversion routine based on the ideas put forth in this report has been developed for use with the PROPER code package. (au).}
place = {Sweden}
year = {1991}
month = {May}
}