Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method
F Durbin - The Computer Journal, 1974 - academic.oup.com
F Durbin
The Computer Journal, 1974•academic.oup.comAn 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 f (t) in terms of F (s) is valid on the whole period 2 T of the
series. As it is proved, this error bound can be set arbitrarily small, and it is always possible …
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 f (t) in terms of F (s) is valid on the whole period 2 T of the
series. As it is proved, this error bound can be set arbitrarily small, and it is always possible …
Abstract
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 f(t) 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.
Oxford University Press