## 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
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## 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}

}

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}

}