Author(s)

A.J. Davies, J.Mushtaq, L.E. Radford and D.Crann

Abstract

The Laplace transform in time has been shown to provide an excellent alternative to the finite difference method for the solution of parabolic problems associated with partial differential equations. An implementation of the Laplace transform method in a parallel environment can provide a concurrent solution process with no communication overhead. The Laplace transform in time, when applied to the diffusion problem, results in a modified Helmholtz equation in the transform space. The diffusion problem is solved in a parallel environment in which the elliptic problem in transform space is solved using finite differences, finite elements, boundary elements, the method of fundamental solutions and Kansa's multiquadric method. Introduction In the numerical s

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