NDLI: Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation

Content Provider	ACM Digital Library
Author	Crump, Kenny S.
Copyright Year	1976
Abstract	A method is presented for numerically inverting a Laplace transform that requires, in addition to the transform function itself, only sine, cosine, and exponential functions. The method is conceptually much like the method of Dubner and Abate, which approximates the inverse function by means of a Fourier cosine series. The method presented here, however, differs from theirs in two important respects. First of all, the Fourier series contains additional terms involving the sine function selected such that the error in the approximation is less than that of Dubner and Abate and such that the Fourier series approximates the inverse function on an interval of twice the length of the corresponding interval in Dubner and Abate's method. Second, there is incorporated into the method in this paper a transformation of the approximating series into one that converges very rapidly. In test problems using the method it has routinely been possible to evaluate inverse transforms with considerable accuracy over a wide range of values of the independent variable using a relatively few determinations of the Laplace transform itself.
Starting Page	89
Ending Page	96
Page Count	8
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/321921.321931
Journal	Journal of the ACM (JACM)
Volume Number	23
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1976-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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