Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method | Zendy

F. Durbin | Zendy

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Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method

Author(s) -

F. Durbin

Publication year - 1974

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/17.4.371

Subject(s) - laplace transform , inversion (geology) , exponential function , mathematics , post's inversion formula , inverse , continuation , series (stratigraphy) , algorithm , inverse laplace transform , mathematical analysis , computer science , geometry , green's function for the three variable laplace equation , paleontology , structural basin , programming language , biology

An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method. (Dubner and Abate, 1968). The advantages of this modified procedure are twofold: first, the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t; second, and consequently, the trigonometric series obtained for fit) in terms of F(s) is valid on the whole period 2T of the series. As it is proved, this error bound can be set arbitrarily small, and it is always possible to get good results, even in rather difficult cases. Particular implementations and numerical examples are presented.

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