Abstract
In the solution of diffision-~e problems the Laplace transform method in time provides an alternative to the finite difference method. The advantages compared with the finite difference method are that there is no time-step stability problem and if the solution is required at just one time value then there is no need for the computation of solutions at intermediate times. From a variety of numerical techniques available for the numerical inversion, Stehfest’s method has been the numerical inversion process chosen by most authors in association with the boundary element method. The procedure has been successfidly implemented on a distributed memory architecture using a ‘Single Program Multiple Data’ paradigm on a 512-processor nCUBE machine arranged in a hypercube configuration. The Laplace transform method is applicable to linear problems, for non-linear problems a suitable linearisation process is required.
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