Improvement of accuracy in numerical methods for inverting laplace transforms based on the post-widder formula

Computers and Mathematics with Applications

Volumn 36, Issue 5, 1998, Pages 23-34

  Frolov, G A ^a   Kitaev, M Y ^a  

^a NONE   (Russian Federation)

Author keywords

Enhancement procedure; Extrapolation to the limit; Gaver Stehfest method; Laplace transform; Numerical inversion of transforms; Post Widder method; The Pad approximation

Indexed keywords

APPROXIMATION THEORY; EXTRAPOLATION; FUNCTIONS; INVERSE PROBLEMS; NUMERICAL METHODS; ONE DIMENSIONAL; POLYNOMIALS; PROBLEM SOLVING;

GAVER-STEHFEST METHOD; PADE APPROXIMATION; POST-WIDDER FORMULA;

LAPLACE TRANSFORMS;

EID: 0032165073     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00147-3     Document Type: Article

References (26)

1. nd edition, Wiley, New York, (1971).
2. B. Davies and B. Martin, Numerical inversion of Laplace transforms: A critical evaluation and review of methods, J. Comp. Phys. 33, 1-32, (1979).
3. D.L. Jagerman, An inversion technique for the Laplace transform with applications, Bell Sys. Tech. J. 57, 669-710, (1978).
4. D.P. Gaver, Observing stochastic processes and approximate transform inversion, Oper. Res. 14, 444-459, (1966).
5. D.O. Joyce, Survey of extrapolation processes in numerical analysis, SIAM Rev. 13, 435-490, (1971).
6. H. Stehfest, Numerical inversion of Laplace transforms, Comm. ACM 13, 47-49, (1970).
7. J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10, 5-88, (1992).
8. R. Piessens and M. Branders, Numerical inversion of the Laplace transform using generalized Laguerre polynomials, Proc. IEE 118, 1517-1522, (1971).
9. D.L. Jagerman, An inversion technique for the Laplace transform, Bell Sys. Tech. J. 61, 1995-2002, (1982).
10. G.A. Korn and T.M. Korn, Mathematical Handbook, McGraw-Hill, New York, (1968).
11. G.A. Frolov and M.Y. Kitaev, A problem of numerical inversion of implicitly defined Laplace transforms, Computers Math. Applic., (this issue).
12. C. Lanczos, Applied Analysis, Pitman, London, (1957).
13. J. Keilson and W.R. Nunn, Laguerre transformation as a tool for the numerical solution of integral equations of convolution type, Appl. Math. Comput. 5, 313-359, (1979).
14. V.A. Kochegarov and G.A. Frolov, Markov and Non-Markov Models, (in Russian), Radio i Sviaz, Moscow, (1992).
15. J. Riordan, An Introduction to Combinatorial Analysis, Wiley, New York, (1958).
16. R. Bulirsch and J. Stoer, Numerical treatment of ordinary differential equations by extrapolation methods, Numerische Mathematik 8, 1-13, (1966).
17. W.B. Gragg, On extrapolation algorithms for ordinary initial value problems, SIAM J. Numer. Anal. Ser. B 2, 384-403, (1965).
18. G.I. Marchuk and V. V. Schaidurov, Increasing Accuracy of Difference Schemes, (in Russian), Nauka, Moscow, (1979).
19. J. Wimp, Sequence Transformations and Their Applications, Academic Press, (1981).
20. G.A. Baker, Jr. and P. Graves-Morris, Padé Approximants. Part II: Extensions and Applications, Addison-Wesley, Reading, MA, (1981).
21. R. Bulirsch and J. Stoer, Asymptotic upper and lower bounds for results of extrapolation method, Numerische Mathematik 8, 93-104, (1966).
22. P. Laurent, Un théorème de convergence pour le procédé d'extrapolation de Richardson, C. R. Acad. Sci. Paris 256, 1435-1437, (1963).
23. G.L. Choudhury, D.M. Lucantoni and W. Whitt, Multidimensional transform inversion with application to the transient M/G/1 queue, Annals of Probability 4, 719-740, (1994).
24. N.U. Prabhu, Queues and Inventories, Wiley, New York, (1965).
25. G. Honig and U. Hirdes, A method for the numerical inversion of Laplace transforms, J. Comput. Appl. Math. 10, 113-129, (1984).
26. J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA Journal on Computing 7, 36-43, (1995).