Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
- 1 January 1968
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 15 (1), 115-123
- https://doi.org/10.1145/321439.321446
Abstract
In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed. Because the result inverse function is given as a Fourier cosine series, the procedure requires only about ten FORTRAN statements. Furthermore, it does not require the use of involved algorithms for the generation of any special functions, but uses only cosines and exponentials. The basis of the method hinges on the fact that in evaluating the inverse Laplace transform integral there exists a freedom in choosing the contour of integration. Given certain restrictions, the contour may be any vertical line in the right-half plane. Specifying a line, the integral to be evaluated is essentially a Fourier integral. However, the method is concerned with determining the proper line, so that when the integral (along this line) is approximated, the error is as small as desired by virtue of having chosen the particular contour.Keywords
This publication has 5 references indexed in Scilit:
- Numerical Inversion of Laplace Transforms Using Laguerre FunctionsJournal of the ACM, 1966
- The calculation of Fourier integralsMathematics of Computation, 1966
- An algorithm for the machine calculation of complex Fourier seriesMathematics of Computation, 1965
- Numerical inversion of Laplace transformsCommunications of the ACM, 1960
- Numerical quadrature of Fourier transform integralsMathematics of Computation, 1956