Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
MathSciNet review: 983558
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R10, 44A10

Retrieve articles in all journals with MSC: 65R10, 44A10

Additional Information

Keywords: Laplace transform, inversion
Article copyright: © Copyright 1989 American Mathematical Society