Complex variable and regularization methods of inversion of the Laplace transform

Authors:
D. D. Ang, John Lund and Frank Stenger

Journal:
Math. Comp. **53** (1989), 589-608

MSC:
Primary 65R10; Secondary 44A10

DOI:
https://doi.org/10.1090/S0025-5718-1989-0983558-7

MathSciNet review:
983558

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Abstract: In this paper three methods are derived for approximating *f*, given its Laplace transform *g* on $(0,\infty )$, i.e., $\smallint _0^\infty {f(t)\exp ( - st) dt = g(s)}$. Assuming that $g \in {L^2}(0,\infty )$, the first method is based on a Sinc-like rational approximation of *g*, the second on a Sinc solution of the integral equation $\smallint _0^\infty {f(t)\exp ( - st) dt = g(s)}$ via standard regularization, and the third method is based on first converting $\smallint _0^\infty {f(t)\exp ( - st){\mkern 1mu} dt = g(s)}$ to a convolution integral over $\mathbb {R}$, and then finding a Sinc approximation to *f* via the application of a special regularization procedure to solve the Fourier transform problem. We also obtain bounds on the error of approximation, which depend on both the method of approximation and the regularization parameter.

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Keywords:
Laplace transform,
inversion

Article copyright:
© Copyright 1989
American Mathematical Society