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Algorithm 486: Numerical inversion of Laplace transform [D5]

Published: 01 October 1974 Publication History

Abstract

This work forms part of a thesis presented in Grenoble in March 1972. Improvements made to the Dubner and Abate algorithm for numerical inversion of the Laplace transform [1] have led to results which compare favorably with theirs and those of Bellmann [2], and Stehfest [3]. The Dubner method leads to the approximation formula: ƒ(t) = 2eat/T[1/2Re{F(a)} + ∑k-1 Re{F(a + ikπ/T)}cos(t/T)], (1) where F(s) is the Laplace transform of ƒ(t) and a is positive and greater than the real parts of the singularities of ƒ(t).

References

[1]
Dubner, H., and Abate, J. Numerical inversion of Laplace transforms and the Finite Fourier Transform. J. ACM 15, 1 (Jan. 1968), 115-123.
[2]
Bellmann, R., Kalaba, R., and Lockett, J. Numerical Inversion of the Laplace Transform. American Elsevier, New York, 1966.
[3]
Stehfest, H. Algorithm 368. Numerical inversion of Laplace transform. Comm. ACM 13, 1 (Jan. 1970), 47--49.
[4]
Veillon, F. Quelques methodes nouvelles pour le calcul numique de la transform6e inverse de Laplace. Th. U. de Grenoble, Mar. 1972.
[5]
Wolfson, M.L., and Wright, H.V. Combinatorial of Mthings taken N at a time. Comm. ACM 6, 4 (Apr. 1963), 161.
[6]
Pearson, K. (Ed.). Tables of the Incomplete Beta Function. Cambridge U. Press, Cambridge, England, 1948.
[7]
Lemke, C.E. Bimatrix equilibrium points and mathematical programming. Management Sci. 11 (1965), 681-689.
[8]
Ravindran, A. Computational aspects of Lemke's complementary algorithm applied to linear programs. Opsearch 7 (1970), 241-262.
[9]
Ravindran, A. A comparison of the primal simplex and complementary pivot methods for linear programming. Naval Res. Log. Q. 20 (1972), 95-100.
[10]
Eaves, B.C. On quadratic programming. Management Sci. 17 (1971), 698-711.
[11]
Eaves, B.C. The linear complementarity problem. Management Sci. 17 (1971), 612-634.
[12]
Clasen, R.J. Techniques for automatic tolerance control in linear programming. Comm. ACM9 (1966), 802-803.
[13]
Bultheel, A. Remark on Algorithm 450. Comm. ACM 17, 8 (Aug. 1974), 470.
[14]
Williams, T.J., and Otto, R.E. A generalized chemical processing model for the investigation computer control. A.I.E.E. Trans. 79, P. 1, Communications and Electronics, (1960), 458-473
[15]
Kleme, J., and Vasek, V. Methods for optimizing complex chemical processes. In P roe. 2nd Symp. on Use of Computers in Chemical Engineering, CVTS, IAstinad Labem, Czechoslovakia, Sept. 1973, pp. O 84-O 102

Cited By

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  • (2011)Diffusion approximation as a modelling toolNetwork performance engineering10.5555/1996629.1996653(447-476)Online publication date: 1-Jan-2011
  • (1984)Remark on algorithm 486: Numerical inversion of Laplace transformACM Transactions on Mathematical Software10.1145/1271.31941710:3(354)Online publication date: 28-Aug-1984

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  1. Algorithm 486: Numerical inversion of Laplace transform [D5]

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    Published In

    cover image Communications of the ACM
    Communications of the ACM  Volume 17, Issue 10
    Oct. 1974
    50 pages
    ISSN:0001-0782
    EISSN:1557-7317
    DOI:10.1145/355620
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 01 October 1974
    Published in CACM Volume 17, Issue 10

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    Cited By

    View all
    • (2011)Diffusion approximation as a modelling toolNetwork performance engineering10.5555/1996629.1996653(447-476)Online publication date: 1-Jan-2011
    • (1984)Remark on algorithm 486: Numerical inversion of Laplace transformACM Transactions on Mathematical Software10.1145/1271.31941710:3(354)Online publication date: 28-Aug-1984

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