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 27 articles )

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  1. Mishra, Vinod; Rani, Dimple: Laplace transform inversion using Bernstein operational matrix of integration and its application to differential and integral equations (2020)
  2. Saad, E. I.: Time-varying Brinkman electrophoresis of a charged cylinder-in-cell model (2020)
  3. Rani, Dimple; Mishra, Vinod; Cattani, Carlo: Numerical inverse Laplace transform for solving a class of fractional differential equations (2019)
  4. Wang, Tongke; Gu, Yuesheng; Zhang, Zhiyue: An algorithm for the inversion of Laplace transforms using Puiseux expansions (2018)
  5. Mariarosaria Rizzardi: Algorithm 981: Talbot Suite DE: Application of Modified Talbot’s Method to Solve Differential Problems (2017) not zbMATH
  6. Brzeziński, Dariusz W.; Ostalczyk, Piotr: Numerical calculations accuracy comparison of the inverse Laplace transform algorithms for solutions of fractional order differential equations (2016)
  7. 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)
  8. Dingfelder, Benedict; Weideman, J. A. C.: An improved Talbot method for numerical Laplace transform inversion (2015)
  9. 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)
  10. D’Amore, Luisa: Remarks on numerical algorithms for computing the inverse Laplace transform (2014)
  11. D’Amore, Luisa; Campagna, Rosanna; Mele, Valeria; Murli, Almerico; Rizzardi, Mariarosaria: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion (2013)
  12. 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)
  13. Douglas, C.; Kim, I.; Lee, H.; Sheen, D.: Higher-order schemes for the Laplace transformation method for parabolic problems (2011)
  14. Gil, Amparo; Segura, Javier; Temme, Nico M.: Basic methods for computing special functions (2011)
  15. Lee, Hyoseop; Sheen, Dongwoo: Laplace transformation method for the Black-Scholes equation (2009)
  16. Zhen, Yubao; Vainchtein, Anna: Dynamics of steps along a martensitic phase boundary. II: Numerical simulations (2008)
  17. Abate, Joseph; Whitt, Ward: A unified framework for numerically inverting Laplace transforms (2006)
  18. den Iseger, Peter: Numerical transform inversion using Gaussian quadrature (2006)
  19. Stpiczyński, Przemysław: A note on the numerical inversion of the Laplace transform (2006)
  20. Kawakatsu, Hiroyuki: Numerical inversion methods for computing approximate (p)-values (2005)

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