Algorithm 682

Algorithm 682: Talbot’s method for the Laplace inversion problem. We describe a FORTRAN implementation, and some related problems, of Talbot’s method which numerically solves the inversion problem of almost arbitrary Laplace transforms by means of special contour integration. The basic idea is to take into account computer precision to derive a special contour where integration will be carried out.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 20 articles )

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  1. Brzeziński, Dariusz W.; Ostalczyk, Piotr: Numerical calculations accuracy comparison of the inverse Laplace transform algorithms for solutions of fractional order differential equations (2016)
  2. Jaradat, H.M.; Jaradat, M.M.M.; Awawdeh, Fadi; Mustafa, Zead; Alsayyed, O.: A new numerical method for heat equation subject to integral specifications (2016)
  3. Dingfelder, Benedict; Weideman, J.A.C.: An improved Talbot method for numerical Laplace transform inversion (2015)
  4. Antonelli, Laura; Corsaro, Stefania; Marino, Zelda; Rizzardi, Mariarosaria: Algorithm 944: Talbot suite: parallel implementations of Talbot’s method for the numerical inversion of Laplace transforms (2014)
  5. D’Amore, Luisa: Remarks on numerical algorithms for computing the inverse Laplace transform (2014)
  6. D’Amore, Luisa; Campagna, Rosanna; Mele, Valeria; Murli, Almerico: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion (2013)
  7. Kano, Patrick O.; Brio, Moysey; Dostert, Paul; Cain, Jon: Dempster-Shafer evidential theory for the automated selection of parameters for Talbot’s method contours and application to matrix exponentiation (2012)
  8. Douglas, C.; Kim, I.; Lee, H.; Sheen, D.: Higher-order schemes for the Laplace transformation method for parabolic problems (2011)
  9. Gil, Amparo; Segura, Javier; Temme, Nico M.: Basic methods for computing special functions (2011)
  10. Zhen, Yubao; Vainchtein, Anna: Dynamics of steps along a martensitic phase boundary. II: Numerical simulations (2008)
  11. Abate, Joseph; Whitt, Ward: A unified framework for numerically inverting Laplace transforms (2006)
  12. den Iseger, Peter: Numerical transform inversion using Gaussian quadrature (2006)
  13. Stpiczyński, Przemysław: A note on the numerical inversion of the Laplace transform (2006)
  14. Kawakatsu, Hiroyuki: Numerical inversion methods for computing approximate $p$-values (2005)
  15. D’Amore, L.; Murli, A.; Rizzardi, M.: An extension of the Henrici formula for Laplace transform inversion (2000)
  16. Vu Kim Tuan; Dinh Thanh Duc: Automatic evaluation of an abscissa of convergence for inverse Laplace transform (2000)
  17. Weideman, J.A.C.: Algorithms for parameter selection in the Weeks method for inverting the Laplace transform (1999)
  18. Rizzardi, M.: A modification of Talbot’s method for the simultaneous approximation of several values of the inverse Laplace transform (1995)
  19. Abate, Joseph; Whitt, Ward: The Fourier-series method for inverting transforms of probability distributions (1992)
  20. Murli, A.; Rizzardi, M.: Algorithm 682: Talbot’s method for the Laplace inversion problem (1990)