Software for an implementation of Weeks' method for the inverse Laplace transform

ABSTRACT

A software package based on a modification of the Weeks' method is presented for calculating function values f(t) of the inverse Laplace transform. This method requires transform values F(z) at arbitrary points in the complex plane, and is suitable when f(t) has continuous derivatives of all orders; it is especially attractive when f(t) is required at a number of different abscissas t.

REFERENCES

• 1: DAVIES, B., AND MARTIN, B. Numerical inversion of the Laplace transform: A survey and comparison of methods. J. Comput. Phys. 33, 1 (Oct. 1979), 1-32.
• 2: B. S. Garbow , G. Giunta , J. N. Lyness , A. Murli, ALGORITHM 662: a Fortran software package for the numerical inversion of the Laplace transform based on Weeks' method, ACM Transactions on Mathematical Software (TOMS), v.14 n.2, p.171-176, June 1988 [doi>10.1145/45054.214375]
• 3: GIUNTA, G., LYNESS, J. N., AND MURLI, A. An implementation of Weeks' method for the inverse Laplace transform problem. ANL/MCS-TM-39, Argonne National Laboratory, Argonne, Ill., Oct. 1984.
• 4: HONIG, G., AND HIRDES, U. Algorithm 27: A method for the numerical inversion of Laplace transforms. J. Cornput. Appl. Math. 10, 1 (Jan. 1984), 113-132.
• 5: J N Lyness , G Giunta, A modification of the weeks method for numerical inversion of the Laplace transform, Mathematics of Computation, v.47 n.175, p.313-322, July 1986 [doi>10.2307/2008097]
• 6: J. N. Lyness , G. Sande, Algorithm 413: ENTCAF and ENTCRE: evaluation of normalized Taylor coefficients of an analytic function, Communications of the ACM, v.14 n.10, p.669-675, Oct. 1971 [doi>10.1145/362759.362820]
• 7: Robert Piessens , Rudi Huysmans, Algorithm 619: automatic numerical inversion of the Laplace transform [D5], ACM Transactions on Mathematical Software (TOMS), v.10 n.3, p.348-353, Sept. 1984 [doi>10.1145/1271.319416]
• 8: William T. Weeks, Numerical Inversion of Laplace Transforms Using Laguerre Functions, Journal of the ACM (JACM), v.13 n.3, p.419-429, July 1966 [doi>10.1145/321341.321351]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.9 Integral Equations
          Subjects: Fredholm equations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Nonlinear approximation
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Finite difference methods

General Terms:
Algorithms