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Numerical Inversion of Laplace Transform with Multiple Precision Using the Complex Domain

Peter Valkó
Organization: Texas A&M University
Department: Harold Vance Department of Petroleum Engineering
URL: http://pumpjack.tamu.edu/~valko/
Joe Abate
Revision date


This package provides only one function: FT. The function calculates the value of the inverse of a Laplace transform at a specified time point. The Laplace transform should be provided as a function ready for multiple-precision evaluation in the complex plane. In other words, approximate numbers (with decimal point) or Mathematica functions starting with the letter 'N' are not allowed. There are two main groups of methods for the numerical inversion of the Laplace transform. One of them uses values of the transform calculated on the real line. Such an algorithm (GWR) is available from MathSource/4738 . This submission falls into the other group of methods, requiring the evaluation of the transform in the complex plane. The best such method is due to Talbot and this realization gives an improved version of his algorithm. Deatils of the algorith are discussed in the paper Abate, J. and Valkó, P. P.: Multi-Precision Laplace Transform Inversion, International Journal of Numerical Methods for Engineering, (2003), accepted for publication (IJNME A1032.C)

*Mathematics > Calculus and Analysis > Differential Equations

Laplace transform, Numerical inversion, Multiple-precision, Talbot method, Complex arithmetic
Related items

*Numerical Laplace Inversion   [in MathSource: Packages and Programs]
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FixedTalbotNumericalLaplaceInversion.m (3.8 KB) - Mathematica Package
FixedTalbotNumericalLaplaceInversionExample.nb (44.7 KB) - Mathematica Notebook