Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
Numerical inversion of Laplace transforms
Communications of the ACM
Algorithm 619: automatic numerical inversion of the Laplace transform [D5]
ACM Transactions on Mathematical Software (TOMS)
Queueing Analysis of the IBM 2314 Disk Storage Facility
Journal of the ACM (JACM)
Busy Period Analysis of a Time-Sharing System: transform inversion
Journal of the ACM (JACM)
Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation
Journal of the ACM (JACM)
An implementation of a Fourier series method for the numerical inversion of the Laplace transform
ACM Transactions on Mathematical Software (TOMS)
Algorithm 486: Numerical inversion of Laplace transform [D5]
Communications of the ACM
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INFORMS Journal on Computing
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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.