PARALLEL TALBOT ALGORITHM FOR DISTRIBUTED-MEMORY MACHINES

Talbot's method is a general numerical method for the inversion of Lap lace Transforms. It uses the Riemann Inversion Formula by approximatin g the value of the inverse Laplace Transform f(t), for t fixed, by mea ns of suitable samples of the Laplace Transform function F(s) in the c omplex plane. In this paper a parallel algorithm for Talbot's method, designed for distributed memory MIMD machines, is introduced to enhanc e the efficiency. It is principally based on a parallel version of the Goertzel-Reinsch algorithm for computing Clenshaw's sums. Such a para llel algorithm allows large scale Laplace inversion problems to be eff iciently solved. An analysis of the stability of the parallel algorith m is also carried out and some experimental results of a 16-node INTEL iPSC/860 implementation are reported.