Algorithm 682: Talbot's method of the Laplace inversion problems

ABSTRACT

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.

REFERENCES

• 1: D. E. Amos, ALGORITHM 644: a portable package for Bessel functions of a complex argument and nonnegative order, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.265-273, Sept. 1986 [doi>10.1145/7921.214331]
• 2: DAVIES, B., AND MARTIN, B. Numerical inversion of the Laplace transform: A survey and comparison of methods. J. Comput. Phys. 33 (1979).
• 3: P. A. Fox , A. D. Hall , N. L. Schryer, Algorithm 528: Framework for a Portable Library [Z], ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.177-188, June 1978 [doi>10.1145/355780.355789]
• 4: MURLI, A., AND RIZZARDI, M. Sull'implementazione del metodo di Talbot per la inversione numerica della Transformata di Laplace--Progetto Finalizzato Informatica del CNR, Rome, Rapporto SOFMAT 10.83, 1983. (In Italian.)
• 5: PIESSENS, R., DE DONCKER-KAPENGA, E., UBERHUBER, C. W., AND KAHANER, D. K. QUADPACK. A Subroutine Package for Automatic Integration. Springer Verlag, New York, 1983.
• 6: 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]
• 7: STOER, J. Introduzione aU'Analisi Numerica, vol. I. Zanichelli, 1976. Original Title: Einfuhrung in die Numerische Mathematik. Springer Verlag, 1972.
• 8: TALBOT, A. The accurate numerical inversion of Laplace transforms. J. Inst. Math. Appl. 23 (1979).

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computation of transforms (e.g., fast Fourier transform)

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Equal interval integration**
      G.1.9 Integral Equations
          Subjects: Fredholm equations

General Terms:
Algorithms