Multi-precision Laplace transform inversion

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 5, 2004, Pages 979-993

  Abate, J ^a   Valko P P ^b  

^a Texas A and M University ^*  (United States)

^b Texas A M University   (United States)

Author keywords

Laplace transform; Multi precision; Numerical inversion

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS;

FIXED TABLOT (FT) METHOD; GRAVER-WYNN-RHO (GWR) ALGORITHM;

LAPLACE TRANSFORMS;

LAPLACE TRANSFORM; MATHEMATICAL METHOD;

EID: 2942738939     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.995     Document Type: Article

References (22)

1. Davies B, Martin B. Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal of Computational Physics 1979; 33:1-32.
2. Narayanan GV, Beskos DE. Numerical operational methods for time-dependent linear problems. International Journal for Numerical Methods in Engineering 1982; 18:1829-1854.
3. Duffy DG. On the numerical inversion of Laplace Transform: comparison of three new methods on characteristic problems from applications. ACM Transactions on Mathematical Software 1993; 19:333-359.
4. Valkó PP, Vojta BL. The List. 2001; http://pmnpjack.tamu.edu/~valko
5. Koizumi S. A new method of evaluation of the Heaviside operation expression by Fourier series. Philosophical Magazine 1935; 10:1061-1076.
6. Abate J. Whitt W. The Fourier-series method for inverting transforms of probability distributions. Queueing Systems 1992; 10:5-98.
7. D'Amore L, Lacetti G, Murli A. An implementation of a Fourier-series method for the numerical inversion of the Laplace transform. ACM Transactions on Mathematical Software 1999; 25:279-305.
8. Sakurai T. Numerical inversion of the Laplace transform of functions with discontinuities. Queueing Systems, 2004; to appear.
9. Ward EE. The calculation of transients in dynamical systems. Proceedings of the Cambridge Philosophical Society 1954; 50:49-59.
10. Abate J, Choudhury G, Whitt W. On the Laguerre-method for numerically inverting Laplace transforms. INFORMS Journal of Computing 1996; 8:413 427.
11. Weideman JAC. Algorithms for parameter selection in the Weeks method for inverting the Laplace transform. SIAM Journal on Scientific Computing 1999; 21:111-128.
12. Gaver DP Jr. Observing stochastic processes and approximate transform inversion. Operations Research 1966; 14:444-459.
13. Talbot A. The accurate numerical inversion of Laplace transforms. Journal of the Institute of Mathematics and Its Applications 1979; 23:97-120.
14. Davies B. Integral Transforms and Their Applications (3rd edn). Springer: New York, 2002.
15. Wimp J. Sequence Transformations and Their Applications. Academic Press: New York, 1981.
16. Stehfest H. Algorithm 368: numerical inversion of Laplace transforms. Communications of the ACM 1970; 13:47-49 and 624.
17. Valkó PP, Abate J. Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion. Computational Mathematics and Applications 2004, to appear.
18. Mathematica Information Center, http://library.wolfram.com/database/MathSource/4738/
19. Murli A, Rizzardi M. Algorithm 682. Talbot's method for the Laplace inversion problem. ACM Transactions on Mathematical Software l990; 16:158-168.
20. Evans GA. Numerical inversion of Laplace transforms using optimal contours in the complex plane. International Journal of Computer Mathematics 1993; 49:93-105.
21. Evans GA, Chung KC. Laplace transforms inversion using optimal contours in the complex plane. International Journal of Computer Mathematics 2000; 73:531-543.
22. Doetsch G. Introduction to the Theory and Application of Laplace Transformation. Springer: New York, 1974.