The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
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.
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Citations
Cites
Table of Integrals, Series, and Products
(1980) · Elsevier eBooks · doi:10.1016/c2013-0-10754-4 · Cited by 18,782
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
Table of Integrals, Series, and Products
S., D., Gradshteyn, I. S., & Ryzhik, I. M. (1966) · Mathematics of Computation · doi:10.2307/2003554 · Cited by 8,092
Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
Dubner, H., & Abate, J. (1968) · Journal of the ACM · doi:10.1145/321439.321446 · Cited by 547
Fast Fourier Transforms: for fun and profit
Gentleman, W. M., & Sande, G. (1966) · Proceedings of the November 7-10, 1966, fall joint computer conference on XX - AFIPS '66 (Fall) · doi:10.1145/1464291.1464352 · Cited by 542
Cited by
The Fourier-series method for inverting transforms of probability distributions
Abate, J., & Whitt, W. (1992) · Queueing Systems · doi:10.1007/bf01158520 · Cited by 697
Numerical inversion of the laplace transform: a survey and comparison of methods
Davies, B., & Martin, B. (1979) · Journal of Computational Physics · doi:10.1016/0021-9991(79)90025-1 · Cited by 668
Metadata
- Authors
- Durbin, F.
- Venue
- The Computer Journal
- Publisher
- Oxford University Press (OUP)
- Published
- 1974-11-01
- Volume
- 17
- Issue
- 4
- Pages
- 371-376
- ISSN
- 0010-4620 (ISSN-L)
- 1460-2067
- OpenAlex
- W2171640513
- Cited by
- 1,157
- References
- 5
- FWCI
- 0.65
- Type
- journal article
- Language
- en
- Open access
- closed
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- Durbin, F. (1974). Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method. The Computer Journal. https://doi.org/10.1093/comjnl/17.4.371
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
