Error Analysis of a Laplace Transform Inversion Procedure

Abstract

This paper establishes new results for attaining accuracy and efficiency in a numerical method for inverting Laplace transforms. The method, developed by D. L. Jagerman [Bell System Tech. J., 57 (1978), pp. 669–710]; [op. cit., 61 (1982), pp. 1995–2002], defines a sequence of positive operators from Widder’s inversion formula that generate a sequence of functions, called the approximation sequence, that converge uniformly to the inverse of a transform. Some internal parameters introduced by the method must be properly specified for efficient and accurate computation. Until now, computational instability and slow convergence have been the major drawbacks of the method. The new results change this state of affairs by giving explicit formulas for determining the parameters and controlling instability, thus permitting computations (with high-order terms) of the approximation sequence that ensure convergence.