An implementation of a Fourier series method for the numerical inversion of the Laplace transform

ABSTRACT

Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demonstrate how this expression can be used in the development of an automatic routine, one in which the user needs to specify only the required accuracy.

REFERENCES

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INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms
      G.1.2 Approximation
          Subjects: Nonlinear approximation

General Terms:
Algorithms

Keywords:
Fourier series methods, Laplace transform inversion, automatic stopping criterion